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

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

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

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

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

- e^{- x} cos (e^{- x})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (e^{- x}) = - e^{- x}

= cos (e^{- x}) (- e^{- x})

Simplify

= - e^{- x} cos (e^{- x})

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