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- Derivative of:
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Derivative of (x-2)^4
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Derivative of u
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Derivative of (x-1)/2
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Identical expressions
- arcsin^ five (4x)log2(x- five)
- arc sinus of to the power of 5(4x) logarithm of 2(x minus 5)
- arc sinus of to the power of five (4x) logarithm of 2(x minus five)
- arcsin5(4x)log2(x-5)
- arcsin54xlog2x-5
- arcsin⁵(4x)log2(x-5)
- arcsin^54xlog2x-5
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Similar expressions
- arcsin^5(4x)log2(x+5)
Derivative of arcsin^5(4x)log2(x-5)
The solution
You have entered
[src]
5 log(x - 5)
asin (4*x)*----------
log(2)
$$\frac{\log{\left(x - 5 \right)}}{\log{\left(2 \right)}} \operatorname{asin}^{5}{\left(4 x \right)}$$
asin(4*x)^5*(log(x - 5)/log(2))
The first derivative
[src]
5 4
asin (4*x) 20*asin (4*x)*log(x - 5)
-------------- + ------------------------
(x - 5)*log(2) ___________
/ 2
\/ 1 - 16*x *log(2)
$$\frac{\operatorname{asin}^{5}{\left(4 x \right)}}{\left(x - 5\right) \log{\left(2 \right)}} + \frac{20 \log{\left(x - 5 \right)} \operatorname{asin}^{4}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \log{\left(2 \right)}}$$
The second derivative
[src]
/ 2 \
3 | asin (4*x) / 1 x*asin(4*x) \ 40*asin(4*x) |
asin (4*x)*|- ---------- + 320*|- ---------- + --------------|*log(-5 + x) + -----------------------|
| 2 | 2 3/2| ___________ |
| (-5 + x) | -1 + 16*x / 2\ | / 2 |
\ \ \1 - 16*x / / \/ 1 - 16*x *(-5 + x)/
-----------------------------------------------------------------------------------------------------
log(2)
$$\frac{\left(320 \left(\frac{x \operatorname{asin}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{16 x^{2} - 1}\right) \log{\left(x - 5 \right)} - \frac{\operatorname{asin}^{2}{\left(4 x \right)}}{\left(x - 5\right)^{2}} + \frac{40 \operatorname{asin}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \left(x - 5\right)}\right) \operatorname{asin}^{3}{\left(4 x \right)}}{\log{\left(2 \right)}}$$
The third derivative
[src]
/ / 1 x*asin(4*x) \ \
| 480*|- ---------- + --------------|*asin(4*x)|
| | 2 3/2| |
| 3 / 2 2 2 \ 2 | -1 + 16*x / 2\ | |
2 |asin (4*x) | 12 asin (4*x) 48*x*asin(4*x) 48*x *asin (4*x)| 30*asin (4*x) \ \1 - 16*x / / |
2*asin (4*x)*|---------- + 160*|-------------- + -------------- + -------------- + ----------------|*log(-5 + x) - ------------------------ + ---------------------------------------------|
| 3 | 3/2 3/2 2 5/2 | ___________ -5 + x |
|(-5 + x) |/ 2\ / 2\ / 2\ / 2\ | / 2 2 |
\ \\1 - 16*x / \1 - 16*x / \-1 + 16*x / \1 - 16*x / / \/ 1 - 16*x *(-5 + x) /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(2)
$$\frac{2 \left(160 \left(\frac{48 x^{2} \operatorname{asin}^{2}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{5}{2}}} + \frac{48 x \operatorname{asin}{\left(4 x \right)}}{\left(16 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{12}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(x - 5 \right)} + \frac{480 \left(\frac{x \operatorname{asin}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{16 x^{2} - 1}\right) \operatorname{asin}{\left(4 x \right)}}{x - 5} + \frac{\operatorname{asin}^{3}{\left(4 x \right)}}{\left(x - 5\right)^{3}} - \frac{30 \operatorname{asin}^{2}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \left(x - 5\right)^{2}}\right) \operatorname{asin}^{2}{\left(4 x \right)}}{\log{\left(2 \right)}}$$