What is the derivative of e^{-cos(x}) ?

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

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

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

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\frac{d}{d x} (e^{- c o s (x)})

e^{- c o s (x)} sin (x)

Solution steps

\frac{d}{d x} (e^{- c o s (x)})

Apply the chain rule:

e^{- c o s (x)} \frac{d}{d x} (- cos (x))

= e^{- c o s (x)} \frac{d}{d x} (- cos (x))

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

= e^{- c o s (x)} sin (x)

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