What is the derivative of x*e^{4x} ?

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

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

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

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\frac{d}{d x} (x \cdot 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

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

\int \frac{( e ^{x} - 3 )}{x} d x

\int cos (n t) d t

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

91 - 90 e^{- 0.2 t}

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