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Step-by-step Solution

Derive the function $arccos\left(\sin\left(x\right)\right)$ with respect to x

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Answer

$\frac{-1}{\cos\left(x\right)}\cos\left(x\right)$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(arccos\left(\sin\left(x\right)\right)\right)$
1

Taking the derivative of arccosine

$\frac{-1}{\sqrt{1-\sin\left(x\right)^2}}\cdot\frac{d}{dx}\left(\sin\left(x\right)\right)$
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The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if ${f(x) = \sin(x)}$, then ${f'(x) = \cos(x)\cdot D_x(x)}$

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

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Answer

$\frac{-1}{\cos\left(x\right)}\cos\left(x\right)$
$\frac{d}{dx}\left(arccos\left(\sin\left(x\right)\right)\right)$

Main topic:

Differential calculus

Time to solve it:

~ 0.74 seconds

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