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Popular >

derivative of y=x^5*e^x

Solution

derivative of

y = x^{5} \cdot e^{x}

Solution

5 x^{4} e^{x} + e^{x} x^{5}

Solution steps

\frac{d}{d x} (x^{5} e^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{5}, g = e^{x}

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

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

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

= 5 x^{4} e^{x} + e^{x} x^{5}

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Frequently Asked Questions (FAQ)

What is the derivative of y=x^5*e^x ?
The derivative of y=x^5*e^x is 5x^4e^x+e^xx^5
What is the first derivative of y=x^5*e^x ?
The first derivative of y=x^5*e^x is 5x^4e^x+e^xx^5