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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int_{- 4}^{4} \frac{1}{16 + x ^{2}} d x

\frac{d}{d x} (- 8 cos^{3} (x))

\int 1 - x^{2} - 3 x^{5} d x

x^{2} - 5 x

\frac{5 s}{( s + 7 ) ( s ^{2} + 4 )}

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