Function
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| Derivative
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49 x^{2} \sin{\left(3 x \right)} \cos{\left(9 x \right)} | - 441 x^{2} \sin{\left(3 x \right)} \sin{\left(9 x \right)} + 147 x^{2} \cos{\left(3 x \right)} \cos{\left(9 x \right)} + 98 x \sin{\left(3 x \right)} \cos{\left(9 x \right)} |
300 x^{6} | 1800 x^{5} |
- \frac{x}{\log{\left(9 x^{2} \right)}} | - \frac{1}{\log{\left(9 x^{2} \right)}} + \frac{2}{\log{\left(9 x^{2} \right)}^{2}} |
- 2 x^{2} e^{9 x^{3}} \log{\left(- 8 x \right)} \sin{\left(9 x^{2} \right)} | - 54 x^{4} e^{9 x^{3}} \log{\left(- 8 x \right)} \sin{\left(9 x^{2} \right)} - 36 x^{3} e^{9 x^{3}} \log{\left(- 8 x \right)} \cos{\left(9 x^{2} \right)} - 4 x e^{9 x^{3}} \log{\left(- 8 x \right)} \sin{\left(9 x^{2} \right)} - 2 x e^{9 x^{3}} \sin{\left(9 x^{2} \right)} |
\frac{\cos{\left(2 x^{3} \right)}}{\cos{\left(7 x^{3} \right)}} | - \frac{6 x^{2} \sin{\left(2 x^{3} \right)}}{\cos{\left(7 x^{3} \right)}} + \frac{21 x^{2} \sin{\left(7 x^{3} \right)} \cos{\left(2 x^{3} \right)}}{\cos^{2}{\left(7 x^{3} \right)}} |
\frac{e^{- 9 x} e^{- 2 x^{3}}}{\cos{\left(2 x^{2} \right)}} | - \frac{6 x^{2} e^{- 9 x} e^{- 2 x^{3}}}{\cos{\left(2 x^{2} \right)}} + \frac{4 x e^{- 9 x} e^{- 2 x^{3}} \sin{\left(2 x^{2} \right)}}{\cos^{2}{\left(2 x^{2} \right)}} - \frac{9 e^{- 9 x} e^{- 2 x^{3}}}{\cos{\left(2 x^{2} \right)}} |
\frac{35 x^{3} \cos{\left(6 x^{2} \right)}}{8} | - \frac{105 x^{4} \sin{\left(6 x^{2} \right)}}{2} + \frac{105 x^{2} \cos{\left(6 x^{2} \right)}}{8} |
\frac{9 \log{\left(- 6 x^{3} \right)} \sin{\left(5 x \right)}}{2 x^{2}} | \frac{45 \log{\left(- 6 x^{3} \right)} \cos{\left(5 x \right)}}{2 x^{2}} - \frac{9 \log{\left(- 6 x^{3} \right)} \sin{\left(5 x \right)}}{x^{3}} + \frac{27 \sin{\left(5 x \right)}}{2 x^{3}} |
- e^{- 6 x} e^{5 x^{2}} | - 10 x e^{- 6 x} e^{5 x^{2}} + 6 e^{- 6 x} e^{5 x^{2}} |
e^{- 5 x} e^{7 x^{3}} | 21 x^{2} e^{- 5 x} e^{7 x^{3}} - 5 e^{- 5 x} e^{7 x^{3}} |
- \frac{\sin{\left(9 x \right)}}{\cos{\left(5 x \right)}} | - \frac{5 \sin{\left(5 x \right)} \sin{\left(9 x \right)}}{\cos^{2}{\left(5 x \right)}} - \frac{9 \cos{\left(9 x \right)}}{\cos{\left(5 x \right)}} |
- 40 x^{8} e^{- 4 x^{3}} | 480 x^{10} e^{- 4 x^{3}} - 320 x^{7} e^{- 4 x^{3}} |
\cos{\left(10 x \right)} | - 10 \sin{\left(10 x \right)} |
\log{\left(5 x \right)} | \frac{1}{x} |
\frac{\sin{\left(3 x \right)}}{3 x^{2} \sin{\left(3 x^{2} \right)}} | - \frac{2 \sin{\left(3 x \right)} \cos{\left(3 x^{2} \right)}}{x \sin^{2}{\left(3 x^{2} \right)}} + \frac{\cos{\left(3 x \right)}}{x^{2} \sin{\left(3 x^{2} \right)}} - \frac{2 \sin{\left(3 x \right)}}{3 x^{3} \sin{\left(3 x^{2} \right)}} |
- 4 x^{3} e^{- 6 x^{2}} \log{\left(4 x \right)} | 48 x^{4} e^{- 6 x^{2}} \log{\left(4 x \right)} - 12 x^{2} e^{- 6 x^{2}} \log{\left(4 x \right)} - 4 x^{2} e^{- 6 x^{2}} |
- 3 x \log{\left(5 x^{2} \right)} | - 3 \log{\left(5 x^{2} \right)} - 6 |
- \frac{1}{x} | \frac{1}{x^{2}} |
378 x^{5} e^{- 4 x} | - 1512 x^{5} e^{- 4 x} + 1890 x^{4} e^{- 4 x} |
\sin{\left(2 x \right)} \cos{\left(8 x^{3} \right)} | - 24 x^{2} \sin{\left(2 x \right)} \sin{\left(8 x^{3} \right)} + 2 \cos{\left(2 x \right)} \cos{\left(8 x^{3} \right)} |
\frac{4}{3} | 0 |
\frac{\tilde{\infty}}{x \sin{\left(9 x^{3} \right)}} | \frac{\tilde{\infty} x \cos{\left(9 x^{3} \right)}}{\sin^{2}{\left(9 x^{3} \right)}} + \frac{\tilde{\infty}}{x^{2} \sin{\left(9 x^{3} \right)}} |
15 x^{4} | 60 x^{3} |
- 4 x^{3} e^{2 x^{2}} \cos{\left(2 x \right)} \cos{\left(7 x^{2} \right)} | 56 x^{4} e^{2 x^{2}} \sin{\left(7 x^{2} \right)} \cos{\left(2 x \right)} - 16 x^{4} e^{2 x^{2}} \cos{\left(2 x \right)} \cos{\left(7 x^{2} \right)} + 8 x^{3} e^{2 x^{2}} \sin{\left(2 x \right)} \cos{\left(7 x^{2} \right)} - 12 x^{2} e^{2 x^{2}} \cos{\left(2 x \right)} \cos{\left(7 x^{2} \right)} |
- 90 x^{3} | - 270 x^{2} |
- \frac{14 x^{4} e^{6 x^{3}}}{\sin{\left(7 x \right)}} | - \frac{252 x^{6} e^{6 x^{3}}}{\sin{\left(7 x \right)}} + \frac{98 x^{4} e^{6 x^{3}} \cos{\left(7 x \right)}}{\sin^{2}{\left(7 x \right)}} - \frac{56 x^{3} e^{6 x^{3}}}{\sin{\left(7 x \right)}} |
- \frac{e^{- x^{2}}}{\sin{\left(4 x^{3} \right)}} | \frac{12 x^{2} e^{- x^{2}} \cos{\left(4 x^{3} \right)}}{\sin^{2}{\left(4 x^{3} \right)}} + \frac{2 x e^{- x^{2}}}{\sin{\left(4 x^{3} \right)}} |
\frac{e^{- 3 x^{3}} \cos{\left(3 x^{3} \right)}}{50 x^{2}} | - \frac{9 e^{- 3 x^{3}} \sin{\left(3 x^{3} \right)}}{50} - \frac{9 e^{- 3 x^{3}} \cos{\left(3 x^{3} \right)}}{50} - \frac{e^{- 3 x^{3}} \cos{\left(3 x^{3} \right)}}{25 x^{3}} |
\log{\left(5 x \right)} \cos{\left(x^{2} \right)} | - 2 x \log{\left(5 x \right)} \sin{\left(x^{2} \right)} + \frac{\cos{\left(x^{2} \right)}}{x} |
\frac{2 \sin{\left(7 x^{2} \right)}}{x^{2}} | \frac{28 \cos{\left(7 x^{2} \right)}}{x} - \frac{4 \sin{\left(7 x^{2} \right)}}{x^{3}} |
-7 | 0 |
- \frac{e^{- 10 x^{3}}}{12 x^{3}} | \frac{5 e^{- 10 x^{3}}}{2 x} + \frac{e^{- 10 x^{3}}}{4 x^{4}} |
1 | 0 |
- 56 x^{3} | - 168 x^{2} |
- 24 x^{6} e^{- 5 x^{3}} | 360 x^{8} e^{- 5 x^{3}} - 144 x^{5} e^{- 5 x^{3}} |
\frac{\log{\left(- 10 x \right)} \log{\left(3 x^{3} \right)} \cos{\left(x \right)}}{9 x} | - \frac{\log{\left(- 10 x \right)} \log{\left(3 x^{3} \right)} \sin{\left(x \right)}}{9 x} - \frac{\log{\left(- 10 x \right)} \log{\left(3 x^{3} \right)} \cos{\left(x \right)}}{9 x^{2}} + \frac{\log{\left(- 10 x \right)} \cos{\left(x \right)}}{3 x^{2}} + \frac{\log{\left(3 x^{3} \right)} \cos{\left(x \right)}}{9 x^{2}} |
\log{\left(3 x \right)} \sin{\left(10 x^{3} \right)} | 30 x^{2} \log{\left(3 x \right)} \cos{\left(10 x^{3} \right)} + \frac{\sin{\left(10 x^{3} \right)}}{x} |
\frac{9 \log{\left(7 x^{2} \right)}}{2} | \frac{9}{x} |
\frac{80 x^{3}}{3} | 80 x^{2} |
- \frac{\cos{\left(3 x^{2} \right)}}{8 x^{2}} | \frac{3 \sin{\left(3 x^{2} \right)}}{4 x} + \frac{\cos{\left(3 x^{2} \right)}}{4 x^{3}} |
- \frac{\log{\left(3 x^{2} \right)} \cos{\left(4 x^{2} \right)}}{5 x^{3}} | \frac{8 \log{\left(3 x^{2} \right)} \sin{\left(4 x^{2} \right)}}{5 x^{2}} + \frac{3 \log{\left(3 x^{2} \right)} \cos{\left(4 x^{2} \right)}}{5 x^{4}} - \frac{2 \cos{\left(4 x^{2} \right)}}{5 x^{4}} |
0 | 0 |
- \frac{\log{\left(10 x^{2} \right)}}{5 x} | \frac{\log{\left(10 x^{2} \right)}}{5 x^{2}} - \frac{2}{5 x^{2}} |
0 | 0 |
\frac{\sin{\left(10 x \right)} \sin{\left(3 x^{3} \right)}}{\cos{\left(9 x \right)}} | \frac{9 x^{2} \sin{\left(10 x \right)} \cos{\left(3 x^{3} \right)}}{\cos{\left(9 x \right)}} + \frac{9 \sin{\left(9 x \right)} \sin{\left(10 x \right)} \sin{\left(3 x^{3} \right)}}{\cos^{2}{\left(9 x \right)}} + \frac{10 \sin{\left(3 x^{3} \right)} \cos{\left(10 x \right)}}{\cos{\left(9 x \right)}} |
- \frac{e^{- x} \cos{\left(x \right)}}{2 x} | \frac{e^{- x} \sin{\left(x \right)}}{2 x} + \frac{e^{- x} \cos{\left(x \right)}}{2 x} + \frac{e^{- x} \cos{\left(x \right)}}{2 x^{2}} |
- 56 x^{5} e^{x} | - 56 x^{5} e^{x} - 280 x^{4} e^{x} |
3 x^{2} e^{6 x^{2}} | 36 x^{3} e^{6 x^{2}} + 6 x e^{6 x^{2}} |
12 x^{4} | 48 x^{3} |
- \frac{\log{\left(5 x^{2} \right)}}{4 x^{2}} | \frac{\log{\left(5 x^{2} \right)}}{2 x^{3}} - \frac{1}{2 x^{3}} |
- 3 \sin{\left(7 x \right)} | - 21 \cos{\left(7 x \right)} |
\frac{5 x e^{- 4 x} e^{- 3 x^{2}}}{8} | - \frac{15 x^{2} e^{- 4 x} e^{- 3 x^{2}}}{4} - \frac{5 x e^{- 4 x} e^{- 3 x^{2}}}{2} + \frac{5 e^{- 4 x} e^{- 3 x^{2}}}{8} |
\frac{4 x^{2}}{\cos{\left(2 x \right)}} | \frac{8 x^{2} \sin{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{8 x}{\cos{\left(2 x \right)}} |
- 56 x^{4} e^{- 3 x^{2}} | 336 x^{5} e^{- 3 x^{2}} - 224 x^{3} e^{- 3 x^{2}} |
- \frac{21}{2 x} | \frac{21}{2 x^{2}} |
\frac{1}{\log{\left(5 x \right)} \cos{\left(5 x \right)}} | \frac{5 \sin{\left(5 x \right)}}{\log{\left(5 x \right)} \cos^{2}{\left(5 x \right)}} - \frac{1}{x \log{\left(5 x \right)}^{2} \cos{\left(5 x \right)}} |
- \frac{3 x}{\log{\left(9 x^{3} \right)}} | - \frac{3}{\log{\left(9 x^{3} \right)}} + \frac{9}{\log{\left(9 x^{3} \right)}^{2}} |
x^{3} e^{- 4 x^{3}} \sin{\left(x^{3} \right)} | - 12 x^{5} e^{- 4 x^{3}} \sin{\left(x^{3} \right)} + 3 x^{5} e^{- 4 x^{3}} \cos{\left(x^{3} \right)} + 3 x^{2} e^{- 4 x^{3}} \sin{\left(x^{3} \right)} |
- \frac{\cos{\left(5 x^{3} \right)}}{10 x^{2}} | \frac{3 \sin{\left(5 x^{3} \right)}}{2} + \frac{\cos{\left(5 x^{3} \right)}}{5 x^{3}} |
\frac{9 e^{8 x^{3}}}{x^{2}} | 216 e^{8 x^{3}} - \frac{18 e^{8 x^{3}}}{x^{3}} |
\frac{e^{7 x}}{\cos{\left(6 x \right)}} | \frac{6 e^{7 x} \sin{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} + \frac{7 e^{7 x}}{\cos{\left(6 x \right)}} |
- 28 x^{2} \log{\left(4 x \right)} | - 56 x \log{\left(4 x \right)} - 28 x |
\frac{e^{- 3 x^{3}}}{\log{\left(8 x \right)}} | - \frac{9 x^{2} e^{- 3 x^{3}}}{\log{\left(8 x \right)}} - \frac{e^{- 3 x^{3}}}{x \log{\left(8 x \right)}^{2}} |
- 5 x \log{\left(10 x^{2} \right)} | - 5 \log{\left(10 x^{2} \right)} - 10 |
0 | 0 |
0 | 0 |
\frac{6 x^{2}}{\cos{\left(10 x^{2} \right)}} | \frac{120 x^{3} \sin{\left(10 x^{2} \right)}}{\cos^{2}{\left(10 x^{2} \right)}} + \frac{12 x}{\cos{\left(10 x^{2} \right)}} |
- \frac{6 x^{2}}{\log{\left(- 8 x \right)} \log{\left(- 5 x^{2} \right)} \cos{\left(5 x \right)}} | - \frac{30 x^{2} \sin{\left(5 x \right)}}{\log{\left(- 8 x \right)} \log{\left(- 5 x^{2} \right)} \cos^{2}{\left(5 x \right)}} - \frac{12 x}{\log{\left(- 8 x \right)} \log{\left(- 5 x^{2} \right)} \cos{\left(5 x \right)}} + \frac{12 x}{\log{\left(- 8 x \right)} \log{\left(- 5 x^{2} \right)}^{2} \cos{\left(5 x \right)}} + \frac{6 x}{\log{\left(- 8 x \right)}^{2} \log{\left(- 5 x^{2} \right)} \cos{\left(5 x \right)}} |
\frac{x \log{\left(- 3 x^{2} \right)}}{3 \sin{\left(4 x^{3} \right)}} | - \frac{4 x^{3} \log{\left(- 3 x^{2} \right)} \cos{\left(4 x^{3} \right)}}{\sin^{2}{\left(4 x^{3} \right)}} + \frac{\log{\left(- 3 x^{2} \right)}}{3 \sin{\left(4 x^{3} \right)}} + \frac{2}{3 \sin{\left(4 x^{3} \right)}} |
- \frac{x^{4}}{3} | - \frac{4 x^{3}}{3} |
- \frac{3 e^{3 x^{2}}}{5 \log{\left(2 x^{3} \right)}} | - \frac{18 x e^{3 x^{2}}}{5 \log{\left(2 x^{3} \right)}} + \frac{9 e^{3 x^{2}}}{5 x \log{\left(2 x^{3} \right)}^{2}} |
4 x \log{\left(- 10 x^{3} \right)} | 4 \log{\left(- 10 x^{3} \right)} + 12 |
45 x^{5} | 225 x^{4} |
\frac{70 x^{5}}{\cos{\left(7 x \right)}} | \frac{490 x^{5} \sin{\left(7 x \right)}}{\cos^{2}{\left(7 x \right)}} + \frac{350 x^{4}}{\cos{\left(7 x \right)}} |
- \frac{18 x^{2} \sin{\left(8 x^{2} \right)}}{5} | - \frac{288 x^{3} \cos{\left(8 x^{2} \right)}}{5} - \frac{36 x \sin{\left(8 x^{2} \right)}}{5} |
- 5 x \cos{\left(6 x^{2} \right)} | 60 x^{2} \sin{\left(6 x^{2} \right)} - 5 \cos{\left(6 x^{2} \right)} |
\frac{10 x^{2} \log{\left(8 x \right)}}{\log{\left(- 2 x^{3} \right)}} | \frac{20 x \log{\left(8 x \right)}}{\log{\left(- 2 x^{3} \right)}} - \frac{30 x \log{\left(8 x \right)}}{\log{\left(- 2 x^{3} \right)}^{2}} + \frac{10 x}{\log{\left(- 2 x^{3} \right)}} |
\frac{2}{5} | 0 |
\frac{7 x}{2} | \frac{7}{2} |
- 9 x^{4} e^{- 3 x^{3}} \sin{\left(2 x^{2} \right)} | 81 x^{6} e^{- 3 x^{3}} \sin{\left(2 x^{2} \right)} - 36 x^{5} e^{- 3 x^{3}} \cos{\left(2 x^{2} \right)} - 36 x^{3} e^{- 3 x^{3}} \sin{\left(2 x^{2} \right)} |
0 | 0 |
- \frac{7}{5} | 0 |
0 | 0 |
10 x^{6} \log{\left(x \right)} \log{\left(9 x \right)} | 60 x^{5} \log{\left(x \right)} \log{\left(9 x \right)} + 10 x^{5} \log{\left(x \right)} + 10 x^{5} \log{\left(9 x \right)} |
- \frac{\sin{\left(x^{2} \right)}}{\log{\left(- 3 x^{3} \right)}} | - \frac{2 x \cos{\left(x^{2} \right)}}{\log{\left(- 3 x^{3} \right)}} + \frac{3 \sin{\left(x^{2} \right)}}{x \log{\left(- 3 x^{3} \right)}^{2}} |
\frac{\log{\left(7 x^{2} \right)}}{90 x^{3}} | - \frac{\log{\left(7 x^{2} \right)}}{30 x^{4}} + \frac{1}{45 x^{4}} |
- \frac{e^{4 x^{2}}}{7 x^{3}} | - \frac{8 e^{4 x^{2}}}{7 x^{2}} + \frac{3 e^{4 x^{2}}}{7 x^{4}} |
\sin{\left(4 x \right)} \sin{\left(2 x^{2} \right)} | 4 x \sin{\left(4 x \right)} \cos{\left(2 x^{2} \right)} + 4 \sin{\left(2 x^{2} \right)} \cos{\left(4 x \right)} |
- \sin{\left(3 x \right)} \cos{\left(7 x \right)} | 7 \sin{\left(3 x \right)} \sin{\left(7 x \right)} - 3 \cos{\left(3 x \right)} \cos{\left(7 x \right)} |
\frac{\sin{\left(2 x \right)}}{180 x^{5}} | \frac{\cos{\left(2 x \right)}}{90 x^{5}} - \frac{\sin{\left(2 x \right)}}{36 x^{6}} |
\frac{e^{6 x} \log{\left(- 7 x^{3} \right)}}{\log{\left(4 x^{2} \right)} \sin{\left(4 x^{3} \right)}} | - \frac{12 x^{2} e^{6 x} \log{\left(- 7 x^{3} \right)} \cos{\left(4 x^{3} \right)}}{\log{\left(4 x^{2} \right)} \sin^{2}{\left(4 x^{3} \right)}} + \frac{6 e^{6 x} \log{\left(- 7 x^{3} \right)}}{\log{\left(4 x^{2} \right)} \sin{\left(4 x^{3} \right)}} + \frac{3 e^{6 x}}{x \log{\left(4 x^{2} \right)} \sin{\left(4 x^{3} \right)}} - \frac{2 e^{6 x} \log{\left(- 7 x^{3} \right)}}{x \log{\left(4 x^{2} \right)}^{2} \sin{\left(4 x^{3} \right)}} |
- \frac{7 \cos{\left(9 x \right)}}{16 x^{2}} | \frac{63 \sin{\left(9 x \right)}}{16 x^{2}} + \frac{7 \cos{\left(9 x \right)}}{8 x^{3}} |
\frac{\sin{\left(9 x^{2} \right)}}{4 x \log{\left(10 x^{3} \right)}} | \frac{9 \cos{\left(9 x^{2} \right)}}{2 \log{\left(10 x^{3} \right)}} - \frac{\sin{\left(9 x^{2} \right)}}{4 x^{2} \log{\left(10 x^{3} \right)}} - \frac{3 \sin{\left(9 x^{2} \right)}}{4 x^{2} \log{\left(10 x^{3} \right)}^{2}} |
0 | 0 |
- 63 x^{4} e^{x} e^{3 x^{3}} | - 567 x^{6} e^{x} e^{3 x^{3}} - 63 x^{4} e^{x} e^{3 x^{3}} - 252 x^{3} e^{x} e^{3 x^{3}} |
\frac{e^{5 x} e^{- 7 x^{2}} e^{- 7 x^{3}}}{8 x} | - \frac{21 x e^{5 x} e^{- 7 x^{2}} e^{- 7 x^{3}}}{8} - \frac{7 e^{5 x} e^{- 7 x^{2}} e^{- 7 x^{3}}}{4} + \frac{5 e^{5 x} e^{- 7 x^{2}} e^{- 7 x^{3}}}{8 x} - \frac{e^{5 x} e^{- 7 x^{2}} e^{- 7 x^{3}}}{8 x^{2}} |
\frac{x \sin{\left(8 x \right)}}{6 \log{\left(- 10 x \right)}} | \frac{4 x \cos{\left(8 x \right)}}{3 \log{\left(- 10 x \right)}} + \frac{\sin{\left(8 x \right)}}{6 \log{\left(- 10 x \right)}} - \frac{\sin{\left(8 x \right)}}{6 \log{\left(- 10 x \right)}^{2}} |
x^{2} \sin{\left(8 x^{3} \right)} | 24 x^{4} \cos{\left(8 x^{3} \right)} + 2 x \sin{\left(8 x^{3} \right)} |
\frac{e^{9 x}}{4 x^{3}} | \frac{9 e^{9 x}}{4 x^{3}} - \frac{3 e^{9 x}}{4 x^{4}} |
\frac{e^{4 x^{3}}}{6 x} | 2 x e^{4 x^{3}} - \frac{e^{4 x^{3}}}{6 x^{2}} |