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Popular >

derivative of (6x+e^{-x^2})^4

Solution

derivative of

(6 x + e^{- x^{2}})^{4}

Solution

4 (6 x + e^{- x^{2}})^{3} (6 - 2 e^{- x^{2}} x)

Solution steps

\frac{d}{d x} ((6 x + e^{- x^{2}})^{4})

Apply the chain rule:

4 (6 x + e^{- x^{2}})^{3} \frac{d}{d x} (6 x + e^{- x^{2}})

= 4 (6 x + e^{- x^{2}})^{3} \frac{d}{d x} (6 x + e^{- x^{2}})

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

= 4 (6 x + e^{- x^{2}})^{3} (6 - 2 e^{- x^{2}} x)

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Frequently Asked Questions (FAQ)

What is the derivative of (6x+e^{-x^2})^4 ?
The derivative of (6x+e^{-x^2})^4 is 4(6x+e^{-x^2})^3(6-2e^{-x^2}x)
What is the first derivative of (6x+e^{-x^2})^4 ?
The first derivative of (6x+e^{-x^2})^4 is 4(6x+e^{-x^2})^3(6-2e^{-x^2}x)