Mister Exam
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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
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of y=5x-6
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Derivative of x^6*e^x
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Derivative of x^5/5
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Derivative of x^5-5*x^3-20*x
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Identical expressions
- y=x*arctg(x)^ two
- y equally x multiply by arctg(x) squared
- y equally x multiply by arctg(x) to the power of two
- y=x*arctg(x)2
- y=x*arctgx2
- y=x*arctg(x)²
- y=x*arctg(x) to the power of 2
- y=xarctg(x)^2
- y=xarctg(x)2
- y=xarctgx2
- y=xarctgx^2
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Similar expressions
- x^tgx*arctgx^2
Derivative of y=x*arctg(x)^2
The solution
The first derivative
[src]
2 2*x*atan(x)
atan (x) + -----------
2
1 + x
$$\frac{2 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \operatorname{atan}^{2}{\left(x \right)}$$
The second derivative
[src]
/ x*(-1 + 2*x*atan(x))\
2*|2*atan(x) - --------------------|
| 2 |
\ 1 + x /
------------------------------------
2
1 + x
$$\frac{2 \left(- \frac{x \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{x^{2} + 1} + 2 \operatorname{atan}{\left(x \right)}\right)}{x^{2} + 1}$$
The third derivative
[src]
/ / 2 \ \
| | 3*x 4*x *atan(x) | |
-2*|-3 + 2*x*|------ - ------------ + atan(x)| + 6*x*atan(x)|
| | 2 2 | |
\ \1 + x 1 + x / /
-------------------------------------------------------------
2
/ 2\
\1 + x /
$$- \frac{2 \left(2 x \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) + 6 x \operatorname{atan}{\left(x \right)} - 3\right)}{\left(x^{2} + 1\right)^{2}}$$
3-я производная
[src]
/ / 2 \ \
| | 3*x 4*x *atan(x) | |
-2*|-3 + 2*x*|------ - ------------ + atan(x)| + 6*x*atan(x)|
| | 2 2 | |
\ \1 + x 1 + x / /
-------------------------------------------------------------
2
/ 2\
\1 + x /
$$- \frac{2 \left(2 x \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right) + 6 x \operatorname{atan}{\left(x \right)} - 3\right)}{\left(x^{2} + 1\right)^{2}}$$
The graph