What is (\partial)/(\partial x)(cos(e^{-x^2})) ?

The answer to (\partial)/(\partial x)(cos(e^{-x^2})) is 2e^{-x^2}xsin(e^{-x^2})

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(\partial)/(\partial x)(cos(e^{-x^2}))

\frac{\partial}{\partial x} (cos (e^{- x^{2}}))

2 e^{- x^{2}} x sin (e^{- x^{2}})

Solution steps

\frac{\partial}{\partial x} (cos (e^{- x^{2}}))

Apply the chain rule:

- sin (e^{- x^{2}}) \frac{\partial}{\partial x} (e^{- x^{2}})

= - sin (e^{- x^{2}}) \frac{\partial}{\partial x} (e^{- x^{2}})

\frac{\partial}{\partial x} (e^{- x^{2}}) = - 2 e^{- x^{2}} x

= - sin (e^{- x^{2}}) (- 2 e^{- x^{2}} x)

Simplify

= 2 e^{- x^{2}} x sin (e^{- x^{2}})

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What is (\partial)/(\partial x)(cos(e^{-x^2})) ?
The answer to (\partial)/(\partial x)(cos(e^{-x^2})) is 2e^{-x^2}xsin(e^{-x^2})