What is the derivative of (6z+e^{-z^2})^3 ?

The derivative of (6z+e^{-z^2})^3 is 3(6z+e^{-z^2})^2(6-2e^{-z^2}z)

What is the first derivative of (6z+e^{-z^2})^3 ?

The first derivative of (6z+e^{-z^2})^3 is 3(6z+e^{-z^2})^2(6-2e^{-z^2}z)

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derivative of

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

3 (6 z + e^{- z^{2}})^{2} (6 - 2 e^{- z^{2}} z)

Solution steps

\frac{d}{d z} ((6 z + e^{- z^{2}})^{3})

Apply the chain rule:

3 (6 z + e^{- z^{2}})^{2} \frac{d}{d z} (6 z + e^{- z^{2}})

= 3 (6 z + e^{- z^{2}})^{2} \frac{d}{d z} (6 z + e^{- z^{2}})

\frac{d}{d z} (6 z + e^{- z^{2}}) = 6 - 2 e^{- z^{2}} z

= 3 (6 z + e^{- z^{2}})^{2} (6 - 2 e^{- z^{2}} z)

What is the derivative of (6z+e^{-z^2})^3 ?
The derivative of (6z+e^{-z^2})^3 is 3(6z+e^{-z^2})^2(6-2e^{-z^2}z)
What is the first derivative of (6z+e^{-z^2})^3 ?
The first derivative of (6z+e^{-z^2})^3 is 3(6z+e^{-z^2})^2(6-2e^{-z^2}z)