What is the derivative of x^8e^x ?

The derivative of x^8e^x is 8x^7e^x+e^xx^8

What is the first derivative of x^8e^x ?

The first derivative of x^8e^x is 8x^7e^x+e^xx^8

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derivative of

x^{8} e^{x}

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

What is the derivative of x^8e^x ?
The derivative of x^8e^x is 8x^7e^x+e^xx^8
What is the first derivative of x^8e^x ?
The first derivative of x^8e^x is 8x^7e^x+e^xx^8