What is the derivative of xe^{5x} ?

The derivative of xe^{5x} is e^{5x}+5e^{5x}x

What is the first derivative of xe^{5x} ?

The first derivative of xe^{5x} is e^{5x}+5e^{5x}x

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derivative of

x e^{5 x}

e^{5 x} + 5 e^{5 x} x

Solution steps

\frac{d}{d x} (x e^{5 x})

Apply the Product Rule:

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

f = x, g = e^{5 x}

= \frac{d x}{d x} e^{5 x} + \frac{d}{d x} (e^{5 x}) x

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

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= 1 \cdot e^{5 x} + e^{5 x} \cdot 5 x

Simplify

= e^{5 x} + 5 e^{5 x} x

\int \frac{e ^{x + 1}}{x + 1} d x

f (x) = \frac{x ^{2}}{9 + 8 x}

\int x^{5} \cdot e^{x^{3}} d x

\int \frac{x}{x ^{2} x ^{2} - 16} d x

\frac{d}{d x} (tan (5 x^{2}))

What is the derivative of xe^{5x} ?
The derivative of xe^{5x} is e^{5x}+5e^{5x}x
What is the first derivative of xe^{5x} ?
The first derivative of xe^{5x} is e^{5x}+5e^{5x}x