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How to use it?
- Derivative of:
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Derivative of sin(2*x^2+3)
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Derivative of (1+x)/(4-x^2)
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Derivative of -1/(x-1)^2
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Derivative of (1+tan(3*x)^(2))*e^(-x/2)
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Identical expressions
- y=ctg((√x)³)×arcsin²x
- y equally ctg((√x)³)×arc sinus of ²x
- y=ctg√x³×arcsin²x
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Similar expressions
- y=ctg(√x)³×arcsin²x
Derivative of y=ctg((√x)³)×arcsin²x
The solution
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/ 3\ | ___ | 2 cot\\/ x /*asin (x)
$$\cot{\left(\left(\sqrt{x}\right)^{3} \right)} \operatorname{asin}^{2}{\left(x \right)}$$
cot((sqrt(x))^3)*asin(x)^2
The first derivative
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/ 3\ / / 3\\
| ___ | ___ 2 | 2| ___ ||
2*asin(x)*cot\\/ x / 3*\/ x *asin (x)*\-1 - cot \\/ x //
--------------------- + ------------------------------------
________ 2
/ 2
\/ 1 - x
$$\frac{3 \sqrt{x} \left(- \cot^{2}{\left(\left(\sqrt{x}\right)^{3} \right)} - 1\right) \operatorname{asin}^{2}{\left(x \right)}}{2} + \frac{2 \cot{\left(\left(\sqrt{x}\right)^{3} \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
The second derivative
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/ / 3\\ / / 3\\
2 | 2| ___ || | 1 | ___ ||
3*asin (x)*\1 + cot \\/ x //*|- ----- + 6*x*cot\\/ x /| / / 3\\
/ 3\ | ___ | ___ | 2| ___ ||
/ 1 x*asin(x) \ | ___ | \ \/ x / 6*\/ x *\1 + cot \\/ x //*asin(x)
2*|- ------- + -----------|*cot\\/ x / + --------------------------------------------------------- - ----------------------------------
| 2 3/2| 4 ________
| -1 + x / 2\ | / 2
\ \1 - x / / \/ 1 - x
$$- \frac{6 \sqrt{x} \left(\cot^{2}{\left(\left(\sqrt{x}\right)^{3} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{3 \left(6 x \cot{\left(\left(\sqrt{x}\right)^{3} \right)} - \frac{1}{\sqrt{x}}\right) \left(\cot^{2}{\left(\left(\sqrt{x}\right)^{3} \right)} + 1\right) \operatorname{asin}^{2}{\left(x \right)}}{4} + 2 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right) \cot{\left(\left(\sqrt{x}\right)^{3} \right)}$$
The third derivative
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/ / 3\\ / / 3\ / / 3\\ / 3\\ / / 3\\ / / 3\\
2 | 2| ___ || | 1 | ___ | 3/2 | 2| ___ || 3/2 2| ___ || | 2| ___ || | 1 | ___ ||
3*asin (x)*\1 + cot \\/ x //*|- ---- - 18*cot\\/ x / + 18*x *\1 + cot \\/ x // + 36*x *cot \\/ x /| 9*\1 + cot \\/ x //*|- ----- + 6*x*cot\\/ x /|*asin(x)
/ 2 \ / 3\ / / 3\\ | 3/2 | | ___ |
| asin(x) 3*x 3*x *asin(x)| | ___ | ___ | 2| ___ || / 1 x*asin(x) \ \ x / \ \/ x /
2*|----------- + ---------- + ------------|*cot\\/ x / - 9*\/ x *\1 + cot \\/ x //*|- ------- + -----------| - ----------------------------------------------------------------------------------------------------------- + --------------------------------------------------------
| 3/2 2 5/2 | | 2 3/2| 8 ________
|/ 2\ / 2\ / 2\ | | -1 + x / 2\ | / 2
\\1 - x / \-1 + x / \1 - x / / \ \1 - x / / 2*\/ 1 - x
$$- 9 \sqrt{x} \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right) \left(\cot^{2}{\left(\left(\sqrt{x}\right)^{3} \right)} + 1\right) - \frac{3 \left(\cot^{2}{\left(\left(\sqrt{x}\right)^{3} \right)} + 1\right) \left(18 x^{\frac{3}{2}} \left(\cot^{2}{\left(\left(\sqrt{x}\right)^{3} \right)} + 1\right) + 36 x^{\frac{3}{2}} \cot^{2}{\left(\left(\sqrt{x}\right)^{3} \right)} - 18 \cot{\left(\left(\sqrt{x}\right)^{3} \right)} - \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{asin}^{2}{\left(x \right)}}{8} + 2 \left(\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \cot{\left(\left(\sqrt{x}\right)^{3} \right)} + \frac{9 \left(6 x \cot{\left(\left(\sqrt{x}\right)^{3} \right)} - \frac{1}{\sqrt{x}}\right) \left(\cot^{2}{\left(\left(\sqrt{x}\right)^{3} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{2 \sqrt{1 - x^{2}}}$$
The graph