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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int \frac{1}{( x ^{2} + y ^{2} )} d y

x^{0.5}

\frac{d}{d x} (x sin (π x))

\frac{d}{d x} (9 e^{x} (cos (x) - sin (x)))

x \to 0 lim ((1 + 6 x)^{\frac{7}{x}})

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