What is the derivative of x^8e^{6x} ?

The derivative of x^8e^{6x} is 8x^7e^{6x}+e^{6x}*6x^8

What is the first derivative of x^8e^{6x} ?

The first derivative of x^8e^{6x} is 8x^7e^{6x}+e^{6x}*6x^8

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derivative of

x^{8} e^{6 x}

8 x^{7} e^{6 x} + e^{6 x} \cdot 6 x^{8}

Solution steps

\frac{d}{d x} (x^{8} e^{6 x})

Apply the Product Rule:

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

f = x^{8}, g = e^{6 x}

= \frac{d}{d x} (x^{8}) e^{6 x} + \frac{d}{d x} (e^{6 x}) x^{8}

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

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= 8 x^{7} e^{6 x} + e^{6 x} \cdot 6 x^{8}

(2 x^{3})^{^{'}}

\frac{x - 1}{x ^{3}}

\int (x^{2} - 3)^{2} d x

6 8 x^{2} + 9

\frac{d}{d x} (\frac{2 x - 1}{x + 3})

What is the derivative of x^8e^{6x} ?
The derivative of x^8e^{6x} is 8x^7e^{6x}+e^{6x}*6x^8
What is the first derivative of x^8e^{6x} ?
The first derivative of x^8e^{6x} is 8x^7e^{6x}+e^{6x}*6x^8