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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 e^x*x
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Derivative of e^(-5*x)
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Derivative of 1/x^6
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Derivative of 2/(x^2-1)
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Identical expressions
- acrtg(tg^ two *x)
- acrtg(tg squared multiply by x)
- acrtg(tg to the power of two multiply by x)
- acrtg(tg2*x)
- acrtgtg2*x
- acrtg(tg²*x)
- acrtg(tg to the power of 2*x)
- acrtg(tg^2x)
- acrtg(tg2x)
- acrtgtg2x
- acrtgtg^2x
Derivative of acrtg(tg^2*x)
The solution
You have entered
[src]
/ 2 \ atan\tan (x)/
$$\operatorname{atan}{\left(\tan^{2}{\left(x \right)} \right)}$$
atan(tan(x)^2)
The first derivative
[src]
/ 2 \
\2 + 2*tan (x)/*tan(x)
----------------------
4
1 + tan (x)
$$\frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1}$$
The second derivative
[src]
/ 4 / 2 \\
/ 2 \ | 2 4*tan (x)*\1 + tan (x)/|
2*\1 + tan (x)/*|1 + 3*tan (x) - -----------------------|
| 4 |
\ 1 + tan (x) /
---------------------------------------------------------
4
1 + tan (x)
$$\frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{4}{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1} + 3 \tan^{2}{\left(x \right)} + 1\right)}{\tan^{4}{\left(x \right)} + 1}$$
The third derivative
[src]
/ 2 2 \
| 4 / 2 \ / 2 \ 2 / 2 \ 6 |
/ 2 \ | 2 6*tan (x)*\1 + tan (x)/ 5*\1 + tan (x)/ *tan (x) 8*\1 + tan (x)/ *tan (x)|
8*\1 + tan (x)/*|2 + 3*tan (x) - ----------------------- - ------------------------ + ------------------------|*tan(x)
| 4 4 2 |
| 1 + tan (x) 1 + tan (x) / 4 \ |
\ \1 + tan (x)/ /
----------------------------------------------------------------------------------------------------------------------
4
1 + tan (x)
$$\frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{5 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{2}{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{6}{\left(x \right)}}{\left(\tan^{4}{\left(x \right)} + 1\right)^{2}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{4}{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1} + 3 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\tan^{4}{\left(x \right)} + 1}$$