What is the derivative of xe^{4x} ?

The derivative of xe^{4x} is e^{4x}+4e^{4x}x

What is the first derivative of xe^{4x} ?

The first derivative of xe^{4x} is e^{4x}+4e^{4x}x

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derivative of

x e^{4 x}

e^{4 x} + 4 e^{4 x} x

Solution steps

\frac{d}{d x} (x e^{4 x})

Apply the Product Rule:

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

f = x, g = e^{4 x}

= \frac{d x}{d x} e^{4 x} + \frac{d}{d x} (e^{4 x}) x

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

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= 1 \cdot e^{4 x} + e^{4 x} \cdot 4 x

Simplify

= e^{4 x} + 4 e^{4 x} x

\frac{d y}{d x} = x^{2} - y

\int \frac{1}{x ^{2} 49 - x ^{2}} d x

f (x) = x^{2}, at x = 0

\int 7 sin^{2} (t) cos^{4} (t) d t

\frac{( 2 t e ^{- 3 t} )}{5} + 3 t \cdot sin (t)

What is the derivative of xe^{4x} ?
The derivative of xe^{4x} is e^{4x}+4e^{4x}x
What is the first derivative of xe^{4x} ?
The first derivative of xe^{4x} is e^{4x}+4e^{4x}x