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 asin(x)
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Derivative of cos(x^3)
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Derivative of (cos(x))^3
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Derivative of 1/tan(x)
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Identical expressions
- x^ four *atan(3x)
- x to the power of 4 multiply by arc tangent of gent of (3x)
- x to the power of four multiply by arc tangent of gent of (3x)
- x4*atan(3x)
- x4*atan3x
- x⁴*atan(3x)
- x^4atan(3x)
- x4atan(3x)
- x4atan3x
- x^4atan3x
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Similar expressions
- x^4*arctan(3x)
Derivative of x^4*atan(3x)
The solution
You have entered
[src]
4 x *atan(3*x)
$$x^{4} \operatorname{atan}{\left(3 x \right)}$$
x^4*atan(3*x)
The first derivative
[src]
4
3*x 3
-------- + 4*x *atan(3*x)
2
1 + 9*x
$$\frac{3 x^{4}}{9 x^{2} + 1} + 4 x^{3} \operatorname{atan}{\left(3 x \right)}$$
The second derivative
[src]
/ 3 \
2 | 9*x 4*x |
6*x *|2*atan(3*x) - ----------- + --------|
| 2 2|
| / 2\ 1 + 9*x |
\ \1 + 9*x / /
$$6 x^{2} \left(- \frac{9 x^{3}}{\left(9 x^{2} + 1\right)^{2}} + \frac{4 x}{9 x^{2} + 1} + 2 \operatorname{atan}{\left(3 x \right)}\right)$$
The third derivative
[src]
/ / 2 \\
| 3 | 36*x ||
| 9*x *|-1 + --------||
| 3 | 2||
| 108*x 18*x \ 1 + 9*x /|
6*x*|4*atan(3*x) - ----------- + -------- + --------------------|
| 2 2 2 |
| / 2\ 1 + 9*x / 2\ |
\ \1 + 9*x / \1 + 9*x / /
$$6 x \left(\frac{9 x^{3} \left(\frac{36 x^{2}}{9 x^{2} + 1} - 1\right)}{\left(9 x^{2} + 1\right)^{2}} - \frac{108 x^{3}}{\left(9 x^{2} + 1\right)^{2}} + \frac{18 x}{9 x^{2} + 1} + 4 \operatorname{atan}{\left(3 x \right)}\right)$$