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

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

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

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

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\frac{d}{d 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

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{8} x^{\frac{2}{3}} + 9)

\int \frac{( a ^{x} - b ^{x} ) ^{2}}{a ^{x} b ^{x}} d x

\frac{d y}{d x} = e^{7 x - 7 y}

\frac{\partial}{\partial z} (2 z)

y^{^{'}} + y = 1

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