What is the derivative of f(x)=xe^{9x} ?

The derivative of f(x)=xe^{9x} is e^{9x}+9e^{9x}x

What is the first derivative of f(x)=xe^{9x} ?

The first derivative of f(x)=xe^{9x} is e^{9x}+9e^{9x}x

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derivative of

f (x) = 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

x \to 8 lim (\frac{8 x}{x - 8})

y^{^{'}} = (1 - 2 t) y^{2}, y (0) = - \frac{1}{6}

\int x^{3} x^{2} + 24 d x

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

\int_{1}^{2} \frac{5}{2 x - 1} d x

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