What is the derivative of y=e^{-sin(x)} ?

The derivative of y=e^{-sin(x)} is -e^{-sin(x)}cos(x)

What is the first derivative of y=e^{-sin(x)} ?

The first derivative of y=e^{-sin(x)} is -e^{-sin(x)}cos(x)

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derivative of

y = e^{- s i n (x)}

- e^{- s i n (x)} cos (x)

Solution steps

\frac{d}{d x} (e^{- s i n (x)})

Apply the chain rule:

e^{- s i n (x)} \frac{d}{d x} (- sin (x))

= e^{- s i n (x)} \frac{d}{d x} (- sin (x))

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

= e^{- s i n (x)} (- cos (x))

Simplify

= - e^{- s i n (x)} cos (x)

What is the derivative of y=e^{-sin(x)} ?
The derivative of y=e^{-sin(x)} is -e^{-sin(x)}cos(x)
What is the first derivative of y=e^{-sin(x)} ?
The first derivative of y=e^{-sin(x)} is -e^{-sin(x)}cos(x)