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How to use it?
- Derivative of:
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Derivative of 1/x^6
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Derivative of x+lnx
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Derivative of x^2-4*x+3
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Derivative of -(x^2+324)/x
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Identical expressions
- (arctg(x)^ five)*(log(x- three))
- (arctg(x) to the power of 5) multiply by ( logarithm of (x minus 3))
- (arctg(x) to the power of five) multiply by ( logarithm of (x minus three))
- (arctg(x)5)*(log(x-3))
- arctgx5*logx-3
- (arctg(x)⁵)*(log(x-3))
- (arctg(x)^5)(log(x-3))
- (arctg(x)5)(log(x-3))
- arctgx5logx-3
- arctgx^5logx-3
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Similar expressions
- (arctg(x)^5)*(log(x+3))
Derivative of (arctg(x)^5)*(log(x-3))
The solution
You have entered
[src]
5 atan (x)*log(x - 3)
$$\log{\left(x - 3 \right)} \operatorname{atan}^{5}{\left(x \right)}$$
atan(x)^5*log(x - 3)
The first derivative
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5 4
atan (x) 5*atan (x)*log(x - 3)
-------- + ---------------------
x - 3 2
1 + x
$$\frac{5 \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}^{5}{\left(x \right)}}{x - 3}$$
The second derivative
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/ 2 \
3 | atan (x) 10*(-2 + x*atan(x))*log(-3 + x) 10*atan(x) |
atan (x)*|- --------- - ------------------------------- + -----------------|
| 2 2 / 2\ |
| (-3 + x) / 2\ \1 + x /*(-3 + x)|
\ \1 + x / /
$$\left(- \frac{10 \left(x \operatorname{atan}{\left(x \right)} - 2\right) \log{\left(x - 3 \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{10 \operatorname{atan}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{\left(x - 3\right)^{2}}\right) \operatorname{atan}^{3}{\left(x \right)}$$
The third derivative
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/ / 2 2 \ \
| | 2 6 12*x*atan(x) 4*x *atan (x)| |
| 10*|- atan (x) + ------ - ------------ + -------------|*log(-3 + x) |
| 3 2 | 2 2 2 | |
2 |2*atan (x) 15*atan (x) \ 1 + x 1 + x 1 + x / 30*(-2 + x*atan(x))*atan(x)|
atan (x)*|---------- - ------------------ + ------------------------------------------------------------------- - ---------------------------|
| 3 / 2\ 2 2 2 |
|(-3 + x) \1 + x /*(-3 + x) / 2\ / 2\ |
\ \1 + x / \1 + x / *(-3 + x) /
$$\left(\frac{10 \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{6}{x^{2} + 1}\right) \log{\left(x - 3 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{30 \left(x \operatorname{atan}{\left(x \right)} - 2\right) \operatorname{atan}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right)^{2}} - \frac{15 \operatorname{atan}^{2}{\left(x \right)}}{\left(x - 3\right)^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{atan}^{3}{\left(x \right)}}{\left(x - 3\right)^{3}}\right) \operatorname{atan}^{2}{\left(x \right)}$$