What is the derivative of (4z+e^{-z^2})^3 ?

The derivative of (4z+e^{-z^2})^3 is 3(4z+e^{-z^2})^2(4-2e^{-z^2}z)

What is the first derivative of (4z+e^{-z^2})^3 ?

The first derivative of (4z+e^{-z^2})^3 is 3(4z+e^{-z^2})^2(4-2e^{-z^2}z)

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derivative of

(4 z + e^{- z^{2}})^{3}

3 (4 z + e^{- z^{2}})^{2} (4 - 2 e^{- z^{2}} z)

Solution steps

\frac{d}{d z} ((4 z + e^{- z^{2}})^{3})

Apply the chain rule:

3 (4 z + e^{- z^{2}})^{2} \frac{d}{d z} (4 z + e^{- z^{2}})

= 3 (4 z + e^{- z^{2}})^{2} \frac{d}{d z} (4 z + e^{- z^{2}})

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

= 3 (4 z + e^{- z^{2}})^{2} (4 - 2 e^{- z^{2}} z)

What is the derivative of (4z+e^{-z^2})^3 ?
The derivative of (4z+e^{-z^2})^3 is 3(4z+e^{-z^2})^2(4-2e^{-z^2}z)
What is the first derivative of (4z+e^{-z^2})^3 ?
The first derivative of (4z+e^{-z^2})^3 is 3(4z+e^{-z^2})^2(4-2e^{-z^2}z)