Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
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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
- acos(x)*cot(x)
- arc co sinus of e of ine of (x) multiply by cotangent of (x)
- acos(x)cot(x)
- acosxcotx
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Similar expressions
- arccos(x)*cot(x)
- arccosx*cot(x)
Derivative of acos(x)*cot(x)
The solution
You have entered
[src]
acos(x)*cot(x)
$$\cot{\left(x \right)} \operatorname{acos}{\left(x \right)}$$
acos(x)*cot(x)
The first derivative
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/ 2 \ cot(x)
\-1 - cot (x)/*acos(x) - -----------
________
/ 2
\/ 1 - x
$$\left(- \cot^{2}{\left(x \right)} - 1\right) \operatorname{acos}{\left(x \right)} - \frac{\cot{\left(x \right)}}{\sqrt{1 - x^{2}}}$$
The second derivative
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/ 2 \
2*\1 + cot (x)/ x*cot(x) / 2 \
--------------- - ----------- + 2*\1 + cot (x)/*acos(x)*cot(x)
________ 3/2
/ 2 / 2\
\/ 1 - x \1 - x /
$$- \frac{x \cot{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{acos}{\left(x \right)} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{\sqrt{1 - x^{2}}}$$
The third derivative
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/ 2 \
| 3*x |
|-1 + -------|*cot(x)
| 2| / 2 \ / 2 \
\ -1 + x / 6*\1 + cot (x)/*cot(x) / 2 \ / 2 \ 3*x*\1 + cot (x)/
--------------------- - ---------------------- - 2*\1 + cot (x)/*\1 + 3*cot (x)/*acos(x) + -----------------
3/2 ________ 3/2
/ 2\ / 2 / 2\
\1 - x / \/ 1 - x \1 - x /
$$\frac{3 x \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} + 1\right) \operatorname{acos}{\left(x \right)} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \cot{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$$
The graph