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Popular >

derivative of (6x+e^{-x^2}^5)

Solution

\frac{d}{d x} ((6 x + e^{- x^{2}})^{5})

Solution

5 (6 x + e^{- x^{2}})^{4} (6 - 2 e^{- x^{2}} x)

Solution steps

\frac{d}{d x} ((6 x + e^{- x^{2}})^{5})

Apply the chain rule:

5 (6 x + e^{- x^{2}})^{4} \frac{d}{d x} (6 x + e^{- x^{2}})

= 5 (6 x + e^{- x^{2}})^{4} \frac{d}{d x} (6 x + e^{- x^{2}})

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

= 5 (6 x + e^{- x^{2}})^{4} (6 - 2 e^{- x^{2}} x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (6x+e^{-x^2}^5) ?
The derivative of (6x+e^{-x^2}^5) is 5(6x+e^{-x^2})^4(6-2e^{-x^2}x)
What is the first derivative of (6x+e^{-x^2}^5) ?
The first derivative of (6x+e^{-x^2}^5) is 5(6x+e^{-x^2})^4(6-2e^{-x^2}x)