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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of sin(2*x^2+3)
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Derivative of (1+x)/(4-x^2)
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Derivative of -1/(x-1)^2
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Derivative of (1+tan(3*x)^(2))*e^(-x/2)
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Identical expressions
- xarctgx^ three
- xarctgx cubed
- xarctgx to the power of three
- xarctgx3
- xarctgx³
- xarctgx to the power of 3
Derivative of xarctgx^3
The solution
The first derivative
[src]
2
3 3*x*atan (x)
atan (x) + ------------
2
1 + x
$$\frac{3 x \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \operatorname{atan}^{3}{\left(x \right)}$$
The second derivative
[src]
/ x*(-1 + x*atan(x)) \
6*|- ------------------ + atan(x)|*atan(x)
| 2 |
\ 1 + x /
------------------------------------------
2
1 + x
$$\frac{6 \left(- \frac{x \left(x \operatorname{atan}{\left(x \right)} - 1\right)}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
The third derivative
[src]
/ / 2 2 \ \
| | 1 2 6*x*atan(x) 4*x *atan (x)| |
6*|x*|------ - atan (x) - ----------- + -------------| - 3*(-1 + x*atan(x))*atan(x)|
| | 2 2 2 | |
\ \1 + x 1 + x 1 + x / /
------------------------------------------------------------------------------------
2
/ 2\
\1 + x /
$$\frac{6 \left(x \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right) - 3 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}$$