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Popular >

derivative of cos(e^{-2θ^5})

Solution

derivative of

cos (e^{- 2 θ^{5}})

Solution

10 e^{- 2 θ^{5}} θ^{4} sin (e^{- 2 θ^{5}})

Solution steps

\frac{d}{d θ} (cos (e^{- 2 θ^{5}}))

Apply the chain rule:

- sin (e^{- 2 θ^{5}}) \frac{d}{d θ} (e^{- 2 θ^{5}})

= - sin (e^{- 2 θ^{5}}) \frac{d}{d θ} (e^{- 2 θ^{5}})

\frac{d}{d θ} (e^{- 2 θ^{5}}) = - 10 e^{- 2 θ^{5}} θ^{4}

= - sin (e^{- 2 θ^{5}}) (- 10 e^{- 2 θ^{5}} θ^{4})

Simplify

= 10 e^{- 2 θ^{5}} θ^{4} sin (e^{- 2 θ^{5}})

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Frequently Asked Questions (FAQ)

What is the derivative of cos(e^{-2θ^5}) ?
The derivative of cos(e^{-2θ^5}) is 10e^{-2θ^5}θ^4sin(e^{-2θ^5})
What is the first derivative of cos(e^{-2θ^5}) ?
The first derivative of cos(e^{-2θ^5}) is 10e^{-2θ^5}θ^4sin(e^{-2θ^5})