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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 x*x^(1/2)
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Identical expressions
- log10(x- two)*asin^5x
- logarithm of 10(x minus 2) multiply by arc sinus of e of to the power of 5x
- logarithm of 10(x minus two) multiply by arc sinus of e of to the power of 5x
- log10(x-2)*asin5x
- log10x-2*asin5x
- log10(x-2)*asin⁵x
- log10(x-2)asin^5x
- log10(x-2)asin5x
- log10x-2asin5x
- log10x-2asin^5x
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Similar expressions
- log10(x+2)*asin^5x
Derivative of log10(x-2)*asin^5x
The solution
You have entered
[src]
log(x - 2) 5 ----------*asin (x) log(10)
$$\frac{\log{\left(x - 2 \right)}}{\log{\left(10 \right)}} \operatorname{asin}^{5}{\left(x \right)}$$
(log(x - 2)/log(10))*asin(x)^5
The first derivative
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5 4
asin (x) 5*asin (x)*log(x - 2)
--------------- + ---------------------
(x - 2)*log(10) ________
/ 2
\/ 1 - x *log(10)
$$\frac{\operatorname{asin}^{5}{\left(x \right)}}{\left(x - 2\right) \log{\left(10 \right)}} + \frac{5 \log{\left(x - 2 \right)} \operatorname{asin}^{4}{\left(x \right)}}{\sqrt{1 - x^{2}} \log{\left(10 \right)}}$$
The second derivative
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/ 2 \
3 | asin (x) / 4 x*asin(x) \ 10*asin(x) |
asin (x)*|- --------- + 5*|- ------- + -----------|*log(-2 + x) + --------------------|
| 2 | 2 3/2| ________ |
| (-2 + x) | -1 + x / 2\ | / 2 |
\ \ \1 - x / / \/ 1 - x *(-2 + x)/
---------------------------------------------------------------------------------------
log(10)
$$\frac{\left(5 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{4}{x^{2} - 1}\right) \log{\left(x - 2 \right)} - \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(x - 2\right)^{2}} + \frac{10 \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x - 2\right)}\right) \operatorname{asin}^{3}{\left(x \right)}}{\log{\left(10 \right)}}$$
The third derivative
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/ / 4 x*asin(x) \ \
| 15*|- ------- + -----------|*asin(x)|
| | 2 3/2| |
| 3 / 2 2 2 \ 2 | -1 + x / 2\ | |
2 |2*asin (x) | 12 asin (x) 3*x *asin (x) 12*x*asin(x)| 15*asin (x) \ \1 - x / / |
asin (x)*|---------- + 5*|----------- + ----------- + ------------- + ------------|*log(-2 + x) - --------------------- + ------------------------------------|
| 3 | 3/2 3/2 5/2 2 | ________ -2 + x |
|(-2 + x) |/ 2\ / 2\ / 2\ / 2\ | / 2 2 |
\ \\1 - x / \1 - x / \1 - x / \-1 + x / / \/ 1 - x *(-2 + x) /
---------------------------------------------------------------------------------------------------------------------------------------------------------------
log(10)
$$\frac{\left(5 \left(\frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{12}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(x - 2 \right)} + \frac{15 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{4}{x^{2} - 1}\right) \operatorname{asin}{\left(x \right)}}{x - 2} + \frac{2 \operatorname{asin}^{3}{\left(x \right)}}{\left(x - 2\right)^{3}} - \frac{15 \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x - 2\right)^{2}}\right) \operatorname{asin}^{2}{\left(x \right)}}{\log{\left(10 \right)}}$$