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Popular >

derivative of x^8e^{7x}

Solution

derivative of

x^{8} e^{7 x}

Solution

8 x^{7} e^{7 x} + e^{7 x} \cdot 7 x^{8}

Solution steps

\frac{d}{d x} (x^{8} e^{7 x})

Apply the Product Rule:

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

f = x^{8}, g = e^{7 x}

= \frac{d}{d x} (x^{8}) e^{7 x} + \frac{d}{d x} (e^{7 x}) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

= 8 x^{7} e^{7 x} + e^{7 x} \cdot 7 x^{8}

Graph

Popular Examples

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\frac{d}{d x} (e^{\frac{2 x}{3}})

limit as x approaches 0-of 2x^2sin(1/x)

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(\partial)/(\partial x)(sqrt(8+x^2-2y^2))

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Frequently Asked Questions (FAQ)

What is the derivative of x^8e^{7x} ?
The derivative of x^8e^{7x} is 8x^7e^{7x}+e^{7x}*7x^8
What is the first derivative of x^8e^{7x} ?
The first derivative of x^8e^{7x} is 8x^7e^{7x}+e^{7x}*7x^8