What is (\partial)/(\partial x)(xe^{4x}) ?

The answer to (\partial)/(\partial x)(xe^{4x}) is e^{4x}+4e^{4x}x

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(\partial)/(\partial x)(xe^{4x})

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

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

Solution steps

\frac{\partial}{\partial 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{\partial}{\partial x} (x) e^{4 x} + \frac{\partial}{\partial x} (e^{4 x}) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial 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

2 x = y, x + y = 4, x + y = 12

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

t^{2} e^{- t} + (ln (t))^{2}

y = x^{2}, y = \frac{2}{x ^{2} + 1}

x \to 1 - lim (x^{3} - 7 + m)

What is (\partial)/(\partial x)(xe^{4x}) ?
The answer to (\partial)/(\partial x)(xe^{4x}) is e^{4x}+4e^{4x}x