What is the derivative of x^9e^{8x} ?

The derivative of x^9e^{8x} is 9x^8e^{8x}+e^{8x}*8x^9

What is the first derivative of x^9e^{8x} ?

The first derivative of x^9e^{8x} is 9x^8e^{8x}+e^{8x}*8x^9

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\frac{d}{d x} (x^{9} e^{8 x})

9 x^{8} e^{8 x} + e^{8 x} \cdot 8 x^{9}

Solution steps

\frac{d}{d x} (x^{9} e^{8 x})

Apply the Product Rule:

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

f = x^{9}, g = e^{8 x}

= \frac{d}{d x} (x^{9}) e^{8 x} + \frac{d}{d x} (e^{8 x}) x^{9}

\frac{d}{d x} (x^{9}) = 9 x^{8}

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

= 9 x^{8} e^{8 x} + e^{8 x} \cdot 8 x^{9}

What is the derivative of x^9e^{8x} ?
The derivative of x^9e^{8x} is 9x^8e^{8x}+e^{8x}*8x^9
What is the first derivative of x^9e^{8x} ?
The first derivative of x^9e^{8x} is 9x^8e^{8x}+e^{8x}*8x^9