What is the derivative of xe^{8x} ?

The derivative of xe^{8x} is e^{8x}+8e^{8x}x

What is the first derivative of xe^{8x} ?

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

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\frac{d}{d x} (x e^{8 x})

e^{8 x} + 8 e^{8 x} x

Solution steps

\frac{d}{d x} (x e^{8 x})

Apply the Product Rule:

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

f = x, g = e^{8 x}

= \frac{d x}{d x} e^{8 x} + \frac{d}{d x} (e^{8 x}) x

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

\frac{d}{d x} (e^{8 x}) = e^{8 x} \cdot 8

= 1 \cdot e^{8 x} + e^{8 x} \cdot 8 x

Simplify

= e^{8 x} + 8 e^{8 x} x

n = 0 \sum \infty 4^{2 n + 1}

\frac{\partial}{\partial x} (∣ x - y ∣)

\frac{d}{d x} (ln^{4} (\frac{( x ^{2} - 1 ) ^{3}}{x ^{2} - 1}))

\int sin (x) sin (cos (x)) d x

f (x) = 5 - x^{2}, at x = - 1

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