What is the derivative of arcsin(cos(x)) ?

The derivative of arcsin(cos(x)) is -csc(x)sqrt(sin^2(x))

What is the first derivative of arcsin(cos(x)) ?

The first derivative of arcsin(cos(x)) is -csc(x)sqrt(sin^2(x))

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\frac{d}{d x} (arcsin (cos (x)))

- csc (x) sin^{2} (x)

Solution steps

\frac{d}{d x} (arcsin (cos (x)))

Apply the chain rule:

\frac{1}{1 - ( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

= \frac{1}{1 - ( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= \frac{1}{1 - ( cos ( x ) ) ^{2}} (- sin (x))

Simplify

\frac{1}{1 - cos ^{2} ( x )} (- sin (x)) : - csc (x) sin^{2} (x)

= - csc (x) sin^{2} (x)

What is the derivative of arcsin(cos(x)) ?
The derivative of arcsin(cos(x)) is -csc(x)sqrt(sin^2(x))
What is the first derivative of arcsin(cos(x)) ?
The first derivative of arcsin(cos(x)) is -csc(x)sqrt(sin^2(x))