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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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of sqrt(x)*x
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Derivative of sin(x)^(23)
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Derivative of arcsin(1/x)
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Derivative of atan(4*x)^(3)
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Identical expressions
- atan(four *x)^(three)
- arc tangent of gent of (4 multiply by x) to the power of (3)
- arc tangent of gent of (four multiply by x) to the power of (three)
- atan(4*x)(3)
- atan4*x3
- atan(4x)^(3)
- atan(4x)(3)
- atan4x3
- atan4x^3
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Similar expressions
- arctan(4*x)^(3)
Derivative of atan(4*x)^(3)
The solution
The first derivative
[src]
2
12*atan (4*x)
-------------
2
1 + 16*x
$$\frac{12 \operatorname{atan}^{2}{\left(4 x \right)}}{16 x^{2} + 1}$$
The second derivative
[src]
96*(1 - 4*x*atan(4*x))*atan(4*x)
--------------------------------
2
/ 2\
\1 + 16*x /
$$\frac{96 \left(- 4 x \operatorname{atan}{\left(4 x \right)} + 1\right) \operatorname{atan}{\left(4 x \right)}}{\left(16 x^{2} + 1\right)^{2}}$$
The third derivative
[src]
/ 2 2 \
| 1 2 24*x*atan(4*x) 64*x *atan (4*x)|
384*|--------- - atan (4*x) - -------------- + ----------------|
| 2 2 2 |
\1 + 16*x 1 + 16*x 1 + 16*x /
----------------------------------------------------------------
2
/ 2\
\1 + 16*x /
$$\frac{384 \left(\frac{64 x^{2} \operatorname{atan}^{2}{\left(4 x \right)}}{16 x^{2} + 1} - \frac{24 x \operatorname{atan}{\left(4 x \right)}}{16 x^{2} + 1} - \operatorname{atan}^{2}{\left(4 x \right)} + \frac{1}{16 x^{2} + 1}\right)}{\left(16 x^{2} + 1\right)^{2}}$$
The graph