What is the derivative of y=xe^{9x} ?

The derivative of y=xe^{9x} is e^{9x}+9e^{9x}x

What is the first derivative of y=xe^{9x} ?

The first derivative of y=xe^{9x} is e^{9x}+9e^{9x}x

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derivative of

y = x e^{9 x}

e^{9 x} + 9 e^{9 x} x

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{9 x} + e^{9 x} \cdot 9 x

Simplify

= e^{9 x} + 9 e^{9 x} x

What is the derivative of y=xe^{9x} ?
The derivative of y=xe^{9x} is e^{9x}+9e^{9x}x
What is the first derivative of y=xe^{9x} ?
The first derivative of y=xe^{9x} is e^{9x}+9e^{9x}x