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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 sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of 5*x^4-7*x^2-x
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Derivative of 3x-x^2
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Derivative of 4*sqrt(3)*x/3
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Identical expressions
- arcctg(two *x)*arctg(two *x)
- arcctg(2 multiply by x) multiply by arctg(2 multiply by x)
- arcctg(two multiply by x) multiply by arctg(two multiply by x)
- arcctg(2x)arctg(2x)
- arcctg2xarctg2x
Derivative of arcctg(2*x)*arctg(2*x)
The solution
You have entered
[src]
acot(2*x)*atan(2*x)
$$\operatorname{acot}{\left(2 x \right)} \operatorname{atan}{\left(2 x \right)}$$
acot(2*x)*atan(2*x)
The first derivative
[src]
2*atan(2*x) 2*acot(2*x)
- ----------- + -----------
2 2
1 + 4*x 1 + 4*x
$$\frac{2 \operatorname{acot}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{2 \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}$$
The second derivative
[src]
8*(-1 - 2*x*acot(2*x) + 2*x*atan(2*x))
--------------------------------------
2
/ 2\
\1 + 4*x /
$$\frac{8 \left(- 2 x \operatorname{acot}{\left(2 x \right)} + 2 x \operatorname{atan}{\left(2 x \right)} - 1\right)}{\left(4 x^{2} + 1\right)^{2}}$$
The third derivative
[src]
// 2 \ / 2 \ \
|| 16*x | | 16*x | 12*x |
16*||-1 + --------|*acot(2*x) - |-1 + --------|*atan(2*x) + --------|
|| 2| | 2| 2|
\\ 1 + 4*x / \ 1 + 4*x / 1 + 4*x /
---------------------------------------------------------------------
2
/ 2\
\1 + 4*x /
$$\frac{16 \left(\frac{12 x}{4 x^{2} + 1} + \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right) \operatorname{acot}{\left(2 x \right)} - \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right) \operatorname{atan}{\left(2 x \right)}\right)}{\left(4 x^{2} + 1\right)^{2}}$$