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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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Frequently Asked Questions (FAQ)

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