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Step-by-step Solution

Derive the function $arcsin\left(\frac{}{4}\sin\left(x\right)\right)$ with respect to x

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Answer

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

Step-by-step explanation

Problem to solve:

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

Taking the derivative of arcsine

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

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

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

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Answer

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

Main topic:

Differential calculus

Used formulas:

1. See formulas

Time to solve it:

~ 0.94 seconds

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