Using chain rule, what is the derivative of arcsin (sin (x))

Question

Royce Blake

Mathematics

23 April, 11:28

Using chain rule, what is the derivative of arcsin (sin (x))

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Answers (1)

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India Morse · Answer 1

Chain rule:

if

y=y (u) and u=u (x)

The dy/dx = (dv/du) (du/dx)

In our case

y=arcsin (u)

u=sin (x)

dy/du=1/√ (1-u²) = 1/√ (1-sin²x)

du/dx=cos x

dy/dx=cos x / √ (1-sin²x)

Answer: dy/dx=cos x / √ (1-sin²x)