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- Derivative of a implicit defined function
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- Partial derivative of the function
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- Integral Step by Step
- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of x*e^x^2
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Derivative of x/cos(x)
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Derivative of (x+1)/(x-1)
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Derivative of x^3-x^2
- Integral of d{x}:
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arctg(x)/(x^2+1)
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Identical expressions
- arctg(x)/(x^ two + one)
- arctg(x) divide by (x squared plus 1)
- arctg(x) divide by (x to the power of two plus one)
- arctg(x)/(x2+1)
- arctgx/x2+1
- arctg(x)/(x²+1)
- arctg(x)/(x to the power of 2+1)
- arctgx/x^2+1
- arctg(x) divide by (x^2+1)
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Similar expressions
- arctg(x)/(x^2-1)
Derivative of arctg(x)/(x^2+1)
The solution
You have entered
[src]
atan(x) ------- 2 x + 1
$$\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
atan(x)/(x^2 + 1)
The first derivative
[src]
1 2*x*atan(x)
----------------- - -----------
/ 2\ / 2 \ 2
\1 + x /*\x + 1/ / 2 \
\x + 1/
$$- \frac{2 x \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right) \left(x^{2} + 1\right)}$$
The second derivative
[src]
// 2 \ \
|| 4*x | 3*x |
2*||-1 + ------|*atan(x) - ------|
|| 2| 2|
\\ 1 + x / 1 + x /
----------------------------------
2
/ 2\
\1 + x /
$$\frac{2 \left(- \frac{3 x}{x^{2} + 1} + \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}$$
The third derivative
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/ 2 / 2 \ \
| 11*x | 2*x | |
4*|-2 + ------ - 6*x*|-1 + ------|*atan(x)|
| 2 | 2| |
\ 1 + x \ 1 + x / /
-------------------------------------------
3
/ 2\
\1 + x /
$$\frac{4 \left(\frac{11 x^{2}}{x^{2} + 1} - 6 x \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \operatorname{atan}{\left(x \right)} - 2\right)}{\left(x^{2} + 1\right)^{3}}$$