What is the derivative of arccos(sin(x)) ?

The derivative of arccos(sin(x)) is -1

What is the first derivative of arccos(sin(x)) ?

The first derivative of arccos(sin(x)) is -1

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\frac{d}{d x} (arccos (sin (x)))

- 1

Solution steps

\frac{d}{d x} (arccos (sin (x)))

Apply the chain rule:

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

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

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

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

Simplify

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

= - 1

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x \to 1 lim (3 x^{4} - 3 x^{2} + 6)

\int_{0}^{2} \frac{x}{4 - x ^{2}} d x

What is the derivative of arccos(sin(x)) ?
The derivative of arccos(sin(x)) is -1
What is the first derivative of arccos(sin(x)) ?
The first derivative of arccos(sin(x)) is -1