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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 x^(3*x)
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Derivative of ctg3x
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Derivative of y=x^9
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Derivative of cos(x)/5
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Identical expressions
- log(x)*acos(x)
- logarithm of (x) multiply by arc co sinus of e of ine of (x)
- log(x)acos(x)
- logxacosx
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Similar expressions
- log(x)*arccos(x)
- log(x)*arccosx
Derivative of log(x)*acos(x)
The solution
You have entered
[src]
log(x)*acos(x)
$$\log{\left(x \right)} \operatorname{acos}{\left(x \right)}$$
log(x)*acos(x)
The first derivative
[src]
acos(x) log(x)
------- - -----------
x ________
/ 2
\/ 1 - x
$$- \frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x}$$
The second derivative
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/acos(x) 2 x*log(x) \ -|------- + ------------- + -----------| | 2 ________ 3/2| | x / 2 / 2\ | \ x*\/ 1 - x \1 - x / /
$$- (\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{2}})$$
The third derivative
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/ 2 \
| 3*x |
|-1 + -------|*log(x)
| 2|
3 2*acos(x) 3 \ -1 + x /
- ----------- + --------- + -------------- + ---------------------
3/2 3 ________ 3/2
/ 2\ x 2 / 2 / 2\
\1 - x / x *\/ 1 - x \1 - x /
$$\frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \operatorname{acos}{\left(x \right)}}{x^{3}}$$
The graph