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How to use it?
- Derivative of:
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Derivative of x^(-2)
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Derivative of (x^2-1)^3
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Derivative of sqrt(1/x)
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Derivative of sin(x)^(9)
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Identical expressions
- y=ln(one +arctg^2x)
- y equally ln(1 plus arctg squared x)
- y equally ln(one plus arctg squared x)
- y=ln(1+arctg2x)
- y=ln1+arctg2x
- y=ln(1+arctg²x)
- y=ln(1+arctg to the power of 2x)
- y=ln1+arctg^2x
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Similar expressions
- y=ln(1-arctg^2x)
Derivative of y=ln(1+arctg^2x)
The solution
You have entered
[src]
/ 2 \ log\1 + atan (x)/
$$\log{\left(\operatorname{atan}^{2}{\left(x \right)} + 1 \right)}$$
d / / 2 \\ --\log\1 + atan (x)// dx
$$\frac{d}{d x} \log{\left(\operatorname{atan}^{2}{\left(x \right)} + 1 \right)}$$
The first derivative
[src]
2*atan(x) ----------------------- / 2\ / 2 \ \1 + x /*\1 + atan (x)/
$$\frac{2 \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)}$$
The second derivative
[src]
/ 2 \
| 2*atan (x) |
2*|1 - 2*x*atan(x) - ------------|
| 2 |
\ 1 + atan (x)/
----------------------------------
2
/ 2\ / 2 \
\1 + x / *\1 + atan (x)/
$$\frac{2 \left(- 2 x \operatorname{atan}{\left(x \right)} + 1 - \frac{2 \operatorname{atan}^{2}{\left(x \right)}}{\operatorname{atan}^{2}{\left(x \right)} + 1}\right)}{\left(x^{2} + 1\right)^{2} \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)}$$
The third derivative
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/ 2 3 2 \
| 3*x 3*atan(x) 4*x *atan(x) 4*atan (x) 6*x*atan (x) |
4*|-atan(x) - ------ - ----------------------- + ------------ + ------------------------ + -----------------------|
| 2 / 2\ / 2 \ 2 2 / 2\ / 2 \|
| 1 + x \1 + x /*\1 + atan (x)/ 1 + x / 2\ / 2 \ \1 + x /*\1 + atan (x)/|
\ \1 + x /*\1 + atan (x)/ /
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2
/ 2\ / 2 \
\1 + x / *\1 + atan (x)/
$$\frac{4 \cdot \left(\frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{3 x}{x^{2} + 1} + \frac{6 x \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)} - \operatorname{atan}{\left(x \right)} - \frac{3 \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)} + \frac{4 \operatorname{atan}^{3}{\left(x \right)}}{\left(x^{2} + 1\right) \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)^{2}}\right)}{\left(x^{2} + 1\right)^{2} \left(\operatorname{atan}^{2}{\left(x \right)} + 1\right)}$$
The graph