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How to use it?
- Derivative of:
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Derivative of (x^2+1)^3
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Derivative of (x+3)/(x-2)
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Derivative of x^2*asinh(x)*acosh(x)
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Derivative of (x-2)^2*(x-4)+5
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Identical expressions
- ctg^ three (4x)*arcsin(sqrtx)
- ctg cubed (4x) multiply by arc sinus of ( square root of x)
- ctg to the power of three (4x) multiply by arc sinus of ( square root of x)
- ctg^3(4x)*arcsin(√x)
- ctg3(4x)*arcsin(sqrtx)
- ctg34x*arcsinsqrtx
- ctg³(4x)*arcsin(sqrtx)
- ctg to the power of 3(4x)*arcsin(sqrtx)
- ctg^3(4x)arcsin(sqrtx)
- ctg3(4x)arcsin(sqrtx)
- ctg34xarcsinsqrtx
- ctg^34xarcsinsqrtx
Derivative of ctg^3(4x)*arcsin(sqrtx)
The solution
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3 / ___\ cot (4*x)*asin\\/ x /
$$\cot^{3}{\left(4 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}$$
cot(4*x)^3*asin(sqrt(x))
The first derivative
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3
2 / 2 \ / ___\ cot (4*x)
cot (4*x)*\-12 - 12*cot (4*x)/*asin\\/ x / + -----------------
___ _______
2*\/ x *\/ 1 - x
$$\left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\cot^{3}{\left(4 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
The second derivative
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/ 2 /1 1 \\ | / 2 \ cot (4*x)*|- + ------|| | / 2 \ / 2 \ / ___\ 12*\1 + cot (4*x)/*cot(4*x) \x -1 + x/| |96*\1 + cot (4*x)/*\1 + 2*cot (4*x)/*asin\\/ x / - --------------------------- - ----------------------|*cot(4*x) | ___ _______ ___ _______ | \ \/ x *\/ 1 - x 4*\/ x *\/ 1 - x /
$$\left(96 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \operatorname{asin}{\left(\sqrt{x} \right)} - \frac{\left(\frac{1}{x - 1} + \frac{1}{x}\right) \cot^{2}{\left(4 x \right)}}{4 \sqrt{x} \sqrt{1 - x}} - \frac{12 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)}}{\sqrt{x} \sqrt{1 - x}}\right) \cot{\left(4 x \right)}$$
The third derivative
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3 /3 3 2 \
cot (4*x)*|-- + --------- + ----------| 2 / 2 \ /1 1 \
/ 2 \ | 2 2 x*(-1 + x)| 9*cot (4*x)*\1 + cot (4*x)/*|- + ------| / 2 \ / 2 \
/ 2 \ |/ 2 \ 4 2 / 2 \| / ___\ \x (-1 + x) / \x -1 + x/ 144*\1 + cot (4*x)/*\1 + 2*cot (4*x)/*cot(4*x)
- 384*\1 + cot (4*x)/*\\1 + cot (4*x)/ + 2*cot (4*x) + 7*cot (4*x)*\1 + cot (4*x)//*asin\\/ x / + --------------------------------------- + ---------------------------------------- + ----------------------------------------------
___ _______ ___ _______ ___ _______
8*\/ x *\/ 1 - x \/ x *\/ 1 - x \/ x *\/ 1 - x
$$- 384 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(\left(\cot^{2}{\left(4 x \right)} + 1\right)^{2} + 7 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)} + 2 \cot^{4}{\left(4 x \right)}\right) \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{9 \left(\frac{1}{x - 1} + \frac{1}{x}\right) \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)}}{\sqrt{x} \sqrt{1 - x}} + \frac{144 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)}}{\sqrt{x} \sqrt{1 - x}} + \frac{\left(\frac{3}{\left(x - 1\right)^{2}} + \frac{2}{x \left(x - 1\right)} + \frac{3}{x^{2}}\right) \cot^{3}{\left(4 x \right)}}{8 \sqrt{x} \sqrt{1 - x}}$$