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Popular >

derivative of (4z+e^{-z^2})^5

Solution

derivative of

(4 z + e^{- z^{2}})^{5}

Solution

5 (4 z + e^{- z^{2}})^{4} (4 - 2 e^{- z^{2}} z)

Solution steps

\frac{d}{d z} ((4 z + e^{- z^{2}})^{5})

Apply the chain rule:

5 (4 z + e^{- z^{2}})^{4} \frac{d}{d z} (4 z + e^{- z^{2}})

= 5 (4 z + e^{- z^{2}})^{4} \frac{d}{d z} (4 z + e^{- z^{2}})

\frac{d}{d z} (4 z + e^{- z^{2}}) = 4 - 2 e^{- z^{2}} z

= 5 (4 z + e^{- z^{2}})^{4} (4 - 2 e^{- z^{2}} z)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (4z+e^{-z^2})^5 ?
The derivative of (4z+e^{-z^2})^5 is 5(4z+e^{-z^2})^4(4-2e^{-z^2}z)
What is the first derivative of (4z+e^{-z^2})^5 ?
The first derivative of (4z+e^{-z^2})^5 is 5(4z+e^{-z^2})^4(4-2e^{-z^2}z)