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Popular >

derivative of f(x)=x^5e^{8x}

Solution

derivative of

f (x) = x^{5} e^{8 x}

Solution

5 x^{4} e^{8 x} + e^{8 x} \cdot 8 x^{5}

Solution steps

\frac{d}{d x} (x^{5} e^{8 x})

Apply the Product Rule:

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

f = x^{5}, g = e^{8 x}

= \frac{d}{d x} (x^{5}) e^{8 x} + \frac{d}{d x} (e^{8 x}) x^{5}

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

\frac{d}{d x} (e^{8 x}) = e^{8 x} \cdot 8

= 5 x^{4} e^{8 x} + e^{8 x} \cdot 8 x^{5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^5e^{8x} ?
The derivative of f(x)=x^5e^{8x} is 5x^4e^{8x}+e^{8x}*8x^5
What is the first derivative of f(x)=x^5e^{8x} ?
The first derivative of f(x)=x^5e^{8x} is 5x^4e^{8x}+e^{8x}*8x^5