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How to use it?
- Derivative of:
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Derivative of 4*e^(2*x)
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Derivative of -(3*pi*cos(pi*t/6))/2
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Derivative of (2x-1)^3
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Derivative of (1-2*x)^3
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Identical expressions
- log four (x- one)*arcsinx^4
- logarithm of 4(x minus 1) multiply by arc sinus of x to the power of 4
- logarithm of four (x minus one) multiply by arc sinus of x to the power of 4
- log4(x-1)*arcsinx4
- log4x-1*arcsinx4
- log4(x-1)*arcsinx⁴
- log4(x-1)arcsinx^4
- log4(x-1)arcsinx4
- log4x-1arcsinx4
- log4x-1arcsinx^4
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Similar expressions
- log4(x+1)*arcsinx^4
Derivative of log4(x-1)*arcsinx^4
The solution
You have entered
[src]
4
log(x - 1)*asin (x)
-------------------
log(4)
$$\frac{\log{\left(x - 1 \right)} \operatorname{asin}^{4}{\left(x \right)}}{\log{\left(4 \right)}}$$
/ 4 \ d |log(x - 1)*asin (x)| --|-------------------| dx\ log(4) /
$$\frac{d}{d x} \frac{\log{\left(x - 1 \right)} \operatorname{asin}^{4}{\left(x \right)}}{\log{\left(4 \right)}}$$
The first derivative
[src]
4 3
asin (x) 4*asin (x)*log(x - 1)
-------------- + ---------------------
(x - 1)*log(4) ________
/ 2
\/ 1 - x *log(4)
$$\frac{\operatorname{asin}^{4}{\left(x \right)}}{\left(x - 1\right) \log{\left(4 \right)}} + \frac{4 \log{\left(x - 1 \right)} \operatorname{asin}^{3}{\left(x \right)}}{\sqrt{- x^{2} + 1} \log{\left(4 \right)}}$$
The second derivative
[src]
/ 2 \
2 | asin (x) / 3 x*asin(x) \ 8*asin(x) |
asin (x)*|- --------- + 4*|- ------- + -----------|*log(-1 + x) + --------------------|
| 2 | 2 3/2| ________ |
| (-1 + x) | -1 + x / 2\ | / 2 |
\ \ \1 - x / / \/ 1 - x *(-1 + x)/
---------------------------------------------------------------------------------------
log(4)
$$\frac{\left(4 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{3}{x^{2} - 1}\right) \log{\left(x - 1 \right)} - \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(x - 1\right)^{2}} + \frac{8 \operatorname{asin}{\left(x \right)}}{\sqrt{- x^{2} + 1} \left(x - 1\right)}\right) \operatorname{asin}^{2}{\left(x \right)}}{\log{\left(4 \right)}}$$
The third derivative
[src]
/ / 3 x*asin(x) \ \
| 6*|- ------- + -----------|*asin(x)|
| | 2 3/2| |
| 3 / 2 2 2 \ 2 | -1 + x / 2\ | |
| asin (x) | 6 asin (x) 3*x *asin (x) 9*x*asin(x)| 6*asin (x) \ \1 - x / / |
2*|--------- + 2*|----------- + ----------- + ------------- + -----------|*log(-1 + x) - --------------------- + -----------------------------------|*asin(x)
| 3 | 3/2 3/2 5/2 2| ________ -1 + x |
|(-1 + x) |/ 2\ / 2\ / 2\ / 2\ | / 2 2 |
\ \\1 - x / \1 - x / \1 - x / \-1 + x / / \/ 1 - x *(-1 + x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------
log(4)
$$\frac{2 \cdot \left(2 \cdot \left(\frac{9 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right) \log{\left(x - 1 \right)} + \frac{6 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{3}{x^{2} - 1}\right) \operatorname{asin}{\left(x \right)}}{x - 1} + \frac{\operatorname{asin}^{3}{\left(x \right)}}{\left(x - 1\right)^{3}} - \frac{6 \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{- x^{2} + 1} \left(x - 1\right)^{2}}\right) \operatorname{asin}{\left(x \right)}}{\log{\left(4 \right)}}$$
The graph