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How to use it?
- Derivative of:
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Derivative of 4/x^3
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Derivative of (x+3)^2*(x+5)-1
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Derivative of x^3+2
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Derivative of x^(-2)
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Identical expressions
- arcctg(2x- three)*cos^4x
- arcctg(2x minus 3) multiply by co sinus of e of to the power of 4x
- arcctg(2x minus three) multiply by co sinus of e of to the power of 4x
- arcctg(2x-3)*cos4x
- arcctg2x-3*cos4x
- arcctg(2x-3)*cos⁴x
- arcctg(2x-3)cos^4x
- arcctg(2x-3)cos4x
- arcctg2x-3cos4x
- arcctg2x-3cos^4x
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Similar expressions
- arcctg(2x+3)*cos^4x
Derivative of arcctg(2x-3)*cos^4x
The solution
You have entered
[src]
4 acot(2*x - 3)*cos (x)
$$\cos^{4}{\left(x \right)} \operatorname{acot}{\left(2 x - 3 \right)}$$
acot(2*x - 3)*cos(x)^4
The first derivative
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4
2*cos (x) 3
- -------------- - 4*cos (x)*acot(2*x - 3)*sin(x)
2
1 + (2*x - 3)
$$- 4 \sin{\left(x \right)} \cos^{3}{\left(x \right)} \operatorname{acot}{\left(2 x - 3 \right)} - \frac{2 \cos^{4}{\left(x \right)}}{\left(2 x - 3\right)^{2} + 1}$$
The second derivative
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/ 2 \
2 |/ 2 2 \ 2*cos (x)*(-3 + 2*x) 4*cos(x)*sin(x)|
4*cos (x)*|\- cos (x) + 3*sin (x)/*acot(-3 + 2*x) + -------------------- + ---------------|
| 2 2|
| / 2\ 1 + (-3 + 2*x) |
\ \1 + (-3 + 2*x) / /
$$4 \left(\frac{2 \left(2 x - 3\right) \cos^{2}{\left(x \right)}}{\left(\left(2 x - 3\right)^{2} + 1\right)^{2}} + \left(3 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{acot}{\left(2 x - 3 \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\left(2 x - 3\right)^{2} + 1}\right) \cos^{2}{\left(x \right)}$$
The third derivative
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/ / 2 \ \ | 3 | 4*(-3 + 2*x) | | | 2*cos (x)*|-1 + ---------------| | | | 2| / 2 2 \ 2 | |/ 2 2 \ \ 1 + (-3 + 2*x) / 3*\- cos (x) + 3*sin (x)/*cos(x) 12*cos (x)*(-3 + 2*x)*sin(x)| -8*|\- 5*cos (x) + 3*sin (x)/*acot(-3 + 2*x)*sin(x) + -------------------------------- + -------------------------------- + ----------------------------|*cos(x) | 2 2 2 | | / 2\ 1 + (-3 + 2*x) / 2\ | \ \1 + (-3 + 2*x) / \1 + (-3 + 2*x) / /
$$- 8 \left(\frac{12 \left(2 x - 3\right) \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\left(2 x - 3\right)^{2} + 1\right)^{2}} + \frac{2 \left(\frac{4 \left(2 x - 3\right)^{2}}{\left(2 x - 3\right)^{2} + 1} - 1\right) \cos^{3}{\left(x \right)}}{\left(\left(2 x - 3\right)^{2} + 1\right)^{2}} + \left(3 \sin^{2}{\left(x \right)} - 5 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{acot}{\left(2 x - 3 \right)} + \frac{3 \left(3 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}}{\left(2 x - 3\right)^{2} + 1}\right) \cos{\left(x \right)}$$