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Popular >

derivative of y=2xe^{-x}+2e^{x^5}

Solution

derivative of

y = 2 x e^{- x} + 2 e^{x^{5}}

Solution

2 (e^{- x} - e^{- x} x) + 10 e^{x^{5}} x^{4}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (2 e^{x^{5}}) = 10 e^{x^{5}} x^{4}

= 2 (e^{- x} - e^{- x} x) + 10 e^{x^{5}} x^{4}

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Frequently Asked Questions (FAQ)

What is the derivative of y=2xe^{-x}+2e^{x^5} ?
The derivative of y=2xe^{-x}+2e^{x^5} is 2(e^{-x}-e^{-x}x)+10e^{x^5}x^4
What is the first derivative of y=2xe^{-x}+2e^{x^5} ?
The first derivative of y=2xe^{-x}+2e^{x^5} is 2(e^{-x}-e^{-x}x)+10e^{x^5}x^4