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How to use it?
- Derivative of:
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Derivative of e^2*x
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Derivative of x^sin(x)
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Derivative of sqrt(x^2+1)
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Derivative of 4/x^2
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Identical expressions
- arctan^(eleven)(13x+ seven)
- arc tangent of to the power of (11)(13x plus 7)
- arc tangent of to the power of (eleven)(13x plus seven)
- arctan(11)(13x+7)
- arctan1113x+7
- arctan^1113x+7
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Similar expressions
- arctan^(11)(13x-7)
Derivative of arctan^(11)(13x+7)
The solution
You have entered
[src]
11 atan (13*x + 7)
$$\operatorname{atan}^{11}{\left(13 x + 7 \right)}$$
atan(13*x + 7)^11
The first derivative
[src]
10
143*atan (13*x + 7)
--------------------
2
1 + (13*x + 7)
$$\frac{143 \operatorname{atan}^{10}{\left(13 x + 7 \right)}}{\left(13 x + 7\right)^{2} + 1}$$
The second derivative
[src]
9
3718*atan (7 + 13*x)*(5 - (7 + 13*x)*atan(7 + 13*x))
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2
/ 2\
\1 + (7 + 13*x) /
$$\frac{3718 \left(- \left(13 x + 7\right) \operatorname{atan}{\left(13 x + 7 \right)} + 5\right) \operatorname{atan}^{9}{\left(13 x + 7 \right)}}{\left(\left(13 x + 7\right)^{2} + 1\right)^{2}}$$
The third derivative
[src]
/ 2 2 \
8 | 2 45 30*(7 + 13*x)*atan(7 + 13*x) 4*(7 + 13*x) *atan (7 + 13*x)|
48334*atan (7 + 13*x)*|- atan (7 + 13*x) + --------------- - ---------------------------- + -----------------------------|
| 2 2 2 |
\ 1 + (7 + 13*x) 1 + (7 + 13*x) 1 + (7 + 13*x) /
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2
/ 2\
\1 + (7 + 13*x) /
$$\frac{48334 \left(\frac{4 \left(13 x + 7\right)^{2} \operatorname{atan}^{2}{\left(13 x + 7 \right)}}{\left(13 x + 7\right)^{2} + 1} - \frac{30 \left(13 x + 7\right) \operatorname{atan}{\left(13 x + 7 \right)}}{\left(13 x + 7\right)^{2} + 1} - \operatorname{atan}^{2}{\left(13 x + 7 \right)} + \frac{45}{\left(13 x + 7\right)^{2} + 1}\right) \operatorname{atan}^{8}{\left(13 x + 7 \right)}}{\left(\left(13 x + 7\right)^{2} + 1\right)^{2}}$$