What is the derivative of x^7e^{9x} ?

The derivative of x^7e^{9x} is 7x^6e^{9x}+e^{9x}*9x^7

What is the first derivative of x^7e^{9x} ?

The first derivative of x^7e^{9x} is 7x^6e^{9x}+e^{9x}*9x^7

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\frac{d}{d x} (x^{7} e^{9 x})

7 x^{6} e^{9 x} + e^{9 x} \cdot 9 x^{7}

Solution steps

\frac{d}{d x} (x^{7} e^{9 x})

Apply the Product Rule:

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

f = x^{7}, g = e^{9 x}

= \frac{d}{d x} (x^{7}) e^{9 x} + \frac{d}{d x} (e^{9 x}) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 7 x^{6} e^{9 x} + e^{9 x} \cdot 9 x^{7}

n = 2 \sum \infty \frac{8}{( n ^{2} - 1 )}

\int (4 sin (x) - 1 + 8 x^{- 5}) d x

\int t^{2} - 4 t + 3 d t

\int_{1}^{8} x ln (x) d x

d er i v a t i v e - \frac{12}{x ^{4}}

What is the derivative of x^7e^{9x} ?
The derivative of x^7e^{9x} is 7x^6e^{9x}+e^{9x}*9x^7
What is the first derivative of x^7e^{9x} ?
The first derivative of x^7e^{9x} is 7x^6e^{9x}+e^{9x}*9x^7