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How to use it?
- Derivative of:
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Derivative of (x+5)/(x+1)
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Derivative of x*2^x
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Derivative of e^sin(x)*cos(x)
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Derivative of atan(3*x)
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Identical expressions
- cos(arcsin(four x-8x^4))
- co sinus of e of (arc sinus of (4x minus 8x to the power of 4))
- co sinus of e of (arc sinus of (four x minus 8x to the power of 4))
- cos(arcsin(4x-8x4))
- cosarcsin4x-8x4
- cos(arcsin(4x-8x⁴))
- cosarcsin4x-8x^4
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Similar expressions
- cos(arcsin(4x+8x^4))
Derivative of cos(arcsin(4x-8x^4))
The solution
You have entered
[src]
/ / 4\\ cos\asin\4*x - 8*x //
$$\cos{\left(\operatorname{asin}{\left(- 8 x^{4} + 4 x \right)} \right)}$$
d / / / 4\\\ --\cos\asin\4*x - 8*x /// dx
$$\frac{d}{d x} \cos{\left(\operatorname{asin}{\left(- 8 x^{4} + 4 x \right)} \right)}$$
The first derivative
[src]
/ 3\ / 4\
\4 - 32*x /*\-4*x + 8*x /
-------------------------
___________________
/ 2
/ / 4\
\/ 1 - \4*x - 8*x /
$$\frac{\left(- 32 x^{3} + 4\right) \left(8 x^{4} - 4 x\right)}{\sqrt{- \left(- 8 x^{4} + 4 x\right)^{2} + 1}}$$
The second derivative
[src]
/ 2 2\
| 2 2 / 3\ / 3\ |
|/ 3\ 3 / 3\ 16*x *\-1 + 2*x / *\-1 + 8*x / |
-16*|\-1 + 8*x / + 24*x *\-1 + 2*x / + -------------------------------|
| 2 |
| 2 / 3\ |
\ 1 - 16*x *\1 - 2*x / /
------------------------------------------------------------------------
_______________________
/ 2
/ 2 / 3\
\/ 1 - 16*x *\1 - 2*x /
$$- \frac{16 \cdot \left(\frac{16 x^{2} \left(2 x^{3} - 1\right)^{2} \left(8 x^{3} - 1\right)^{2}}{- 16 x^{2} \left(- 2 x^{3} + 1\right)^{2} + 1} + 24 x^{3} \cdot \left(2 x^{3} - 1\right) + \left(8 x^{3} - 1\right)^{2}\right)}{\sqrt{- 16 x^{2} \left(- 2 x^{3} + 1\right)^{2} + 1}}$$
The third derivative
[src]
/ 3 3 3 2 \
| / 3\ / 3\ 2 / 3\ / 3\ 3 / 3\ / 3\|
| / 3\ / 3\ 2*\-1 + 8*x / *\-1 + 2*x / 32*x *\-1 + 2*x / *\-1 + 8*x / 48*x *\-1 + 2*x / *\-1 + 8*x /|
-384*x*|2*x*\-1 + 2*x / + 3*x*\-1 + 8*x / + -------------------------- + ------------------------------- + ------------------------------|
| 2 2 2 |
| 2 / 3\ / 2\ 2 / 3\ |
| 1 - 16*x *\1 - 2*x / | 2 / 3\ | 1 - 16*x *\1 - 2*x / |
\ \1 - 16*x *\1 - 2*x / / /
------------------------------------------------------------------------------------------------------------------------------------------
_______________________
/ 2
/ 2 / 3\
\/ 1 - 16*x *\1 - 2*x /
$$- \frac{384 x \left(\frac{32 x^{2} \left(2 x^{3} - 1\right)^{3} \left(8 x^{3} - 1\right)^{3}}{\left(- 16 x^{2} \left(- 2 x^{3} + 1\right)^{2} + 1\right)^{2}} + \frac{48 x^{3} \left(2 x^{3} - 1\right)^{2} \cdot \left(8 x^{3} - 1\right)}{- 16 x^{2} \left(- 2 x^{3} + 1\right)^{2} + 1} + \frac{2 \cdot \left(2 x^{3} - 1\right) \left(8 x^{3} - 1\right)^{3}}{- 16 x^{2} \left(- 2 x^{3} + 1\right)^{2} + 1} + 2 x \left(2 x^{3} - 1\right) + 3 x \left(8 x^{3} - 1\right)\right)}{\sqrt{- 16 x^{2} \left(- 2 x^{3} + 1\right)^{2} + 1}}$$
The graph