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

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

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

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

4 (e^{x} + e^{x} x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

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

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

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

Simplify

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

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