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How to use it?
- Derivative of:
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Derivative of 4*e^(2*x)
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Derivative of 2^x+1
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Derivative of 10x
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Derivative of x*lnx
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Identical expressions
- log(x)*atan(five *x)^ four
- logarithm of (x) multiply by arc tangent of gent of (5 multiply by x) to the power of 4
- logarithm of (x) multiply by arc tangent of gent of (five multiply by x) to the power of four
- log(x)*atan(5*x)4
- logx*atan5*x4
- log(x)*atan(5*x)⁴
- log(x)atan(5x)^4
- log(x)atan(5x)4
- logxatan5x4
- logxatan5x^4
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Similar expressions
- log(x)*arctan(5*x)^4
Derivative of log(x)*atan(5*x)^4
The solution
You have entered
[src]
4 log(x)*atan (5*x)
$$\log{\left(x \right)} \operatorname{atan}^{4}{\left(5 x \right)}$$
log(x)*atan(5*x)^4
The first derivative
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4 3
atan (5*x) 20*atan (5*x)*log(x)
---------- + --------------------
x 2
1 + 25*x
$$\frac{20 \log{\left(x \right)} \operatorname{atan}^{3}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{\operatorname{atan}^{4}{\left(5 x \right)}}{x}$$
The second derivative
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/ 2 \
2 | atan (5*x) 100*(-3 + 10*x*atan(5*x))*log(x) 40*atan(5*x)|
atan (5*x)*|- ---------- - -------------------------------- + -------------|
| 2 2 / 2\|
| x / 2\ x*\1 + 25*x /|
\ \1 + 25*x / /
$$\left(- \frac{100 \left(10 x \operatorname{atan}{\left(5 x \right)} - 3\right) \log{\left(x \right)}}{\left(25 x^{2} + 1\right)^{2}} + \frac{40 \operatorname{atan}{\left(5 x \right)}}{x \left(25 x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(5 x \right)}}{x^{2}}\right) \operatorname{atan}^{2}{\left(5 x \right)}$$
The third derivative
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/ / 2 2 \ \ | | 2 3 45*x*atan(5*x) 100*x *atan (5*x)| | | 500*|- atan (5*x) + --------- - -------------- + -----------------|*log(x) | | 3 2 | 2 2 2 | | |atan (5*x) 30*atan (5*x) \ 1 + 25*x 1 + 25*x 1 + 25*x / 150*(-3 + 10*x*atan(5*x))*atan(5*x)| 2*|---------- - -------------- + -------------------------------------------------------------------------- - -----------------------------------|*atan(5*x) | 3 2 / 2\ 2 2 | | x x *\1 + 25*x / / 2\ / 2\ | \ \1 + 25*x / x*\1 + 25*x / /
$$2 \left(\frac{500 \left(\frac{100 x^{2} \operatorname{atan}^{2}{\left(5 x \right)}}{25 x^{2} + 1} - \frac{45 x \operatorname{atan}{\left(5 x \right)}}{25 x^{2} + 1} - \operatorname{atan}^{2}{\left(5 x \right)} + \frac{3}{25 x^{2} + 1}\right) \log{\left(x \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{150 \left(10 x \operatorname{atan}{\left(5 x \right)} - 3\right) \operatorname{atan}{\left(5 x \right)}}{x \left(25 x^{2} + 1\right)^{2}} - \frac{30 \operatorname{atan}^{2}{\left(5 x \right)}}{x^{2} \left(25 x^{2} + 1\right)} + \frac{\operatorname{atan}^{3}{\left(5 x \right)}}{x^{3}}\right) \operatorname{atan}{\left(5 x \right)}$$
The graph