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\frac{d}{dx}\left(arcsin\left(\sin\left(x\right)\cdot\frac{}{4}\right)\right)

Derive the function arcsin(sin(x)/4) with respect to x

Answer

$\frac{\cos\left(x\right)\frac{1}{\sqrt{\frac{^2\left(-1\right)\sin\left(x\right)^2}{16}+1}}}{4}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(arcsin\left(\sin\left(x\right)\cdot\frac{}{4}\right)\right)$
1

Taking the derivative of arcsine

$\frac{d}{dx}\left(\frac{}{4}\sin\left(x\right)\right)\frac{1}{\sqrt{1-\left(\frac{}{4}\sin\left(x\right)\right)^2}}$

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Answer

$\frac{\cos\left(x\right)\frac{1}{\sqrt{\frac{^2\left(-1\right)\sin\left(x\right)^2}{16}+1}}}{4}$
$\frac{d}{dx}\left(arcsin\left(\sin\left(x\right)\cdot\frac{}{4}\right)\right)$

Main topic:

Differential calculus

Used formulas:

2. See formulas

Time to solve it:

~ 0.87 seconds