What is the derivative of e^x+3xe^x ?

The derivative of e^x+3xe^x is 4e^x+3e^xx

What is the first derivative of e^x+3xe^x ?

The first derivative of e^x+3xe^x is 4e^x+3e^xx

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derivative of

e^{x} + 3 x e^{x}

4 e^{x} + 3 e^{x} x

Solution steps

\frac{d}{d x} (e^{x} + 3 x e^{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{x}) + \frac{d}{d x} (3 x e^{x})

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

\frac{d}{d x} (3 x e^{x}) = 3 (e^{x} + e^{x} x)

= e^{x} + 3 (e^{x} + e^{x} x)

Simplify

e^{x} + 3 (e^{x} + e^{x} x) : 4 e^{x} + 3 e^{x} x

= 4 e^{x} + 3 e^{x} x

What is the derivative of e^x+3xe^x ?
The derivative of e^x+3xe^x is 4e^x+3e^xx
What is the first derivative of e^x+3xe^x ?
The first derivative of e^x+3xe^x is 4e^x+3e^xx