Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of 3^x
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Derivative of 2^x
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Derivative of 4
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Derivative of (x^2-1)/(x*3+1)
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Identical expressions
- atan(x)^(two)
- arc tangent of gent of (x) to the power of (2)
- arc tangent of gent of (x) to the power of (two)
- atan(x)(2)
- atanx2
- atanx^2
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Similar expressions
- arctan(x)^(2)
- arctanx^(2)
Derivative of atan(x)^(2)
The solution
You have entered
[src]
2 atan (x)
$$\operatorname{atan}^{2}{\left(x \right)}$$
d / 2 \ --\atan (x)/ dx
$$\frac{d}{d x} \operatorname{atan}^{2}{\left(x \right)}$$
The first derivative
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2*atan(x)
---------
2
1 + x
$$\frac{2 \operatorname{atan}{\left(x \right)}}{x^{2} + 1}$$
The second derivative
[src]
2*(1 - 2*x*atan(x))
-------------------
2
/ 2\
\1 + x /
$$\frac{2 \left(- 2 x \operatorname{atan}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}}$$
The third derivative
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/ 2 \
| 3*x 4*x *atan(x)|
4*|-atan(x) - ------ + ------------|
| 2 2 |
\ 1 + x 1 + x /
------------------------------------
2
/ 2\
\1 + x /
$$\frac{4 \cdot \left(\frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}{\left(x \right)} - \frac{3 x}{x^{2} + 1}\right)}{\left(x^{2} + 1\right)^{2}}$$
The graph