What is the derivative of e^{2x}+2e^{2x}x ?

The derivative of e^{2x}+2e^{2x}x is 4e^{2x}x+4e^{2x}

What is the first derivative of e^{2x}+2e^{2x}x ?

The first derivative of e^{2x}+2e^{2x}x is 4e^{2x}x+4e^{2x}

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derivative of

e^{2 x} + 2 e^{2 x} x

4 e^{2 x} x + 4 e^{2 x}

Solution steps

\frac{d}{d x} (e^{2 x} + 2 e^{2 x} x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{2 x}) + \frac{d}{d x} (2 e^{2 x} x)

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (2 e^{2 x} x) = 2 (2 e^{2 x} x + e^{2 x})

= e^{2 x} \cdot 2 + 2 (2 e^{2 x} x + e^{2 x})

Simplify

e^{2 x} \cdot 2 + 2 (2 e^{2 x} x + e^{2 x}) : 4 e^{2 x} x + 4 e^{2 x}

= 4 e^{2 x} x + 4 e^{2 x}

What is the derivative of e^{2x}+2e^{2x}x ?
The derivative of e^{2x}+2e^{2x}x is 4e^{2x}x+4e^{2x}
What is the first derivative of e^{2x}+2e^{2x}x ?
The first derivative of e^{2x}+2e^{2x}x is 4e^{2x}x+4e^{2x}