What is the derivative of 1/2 e^{2x} ?

The derivative of 1/2 e^{2x} is e^{2x}

What is the first derivative of 1/2 e^{2x} ?

The first derivative of 1/2 e^{2x} is e^{2x}

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derivative of

\frac{1}{2} e^{2 x}

e^{2 x}

Solution steps

\frac{d}{d x} (\frac{1}{2} e^{2 x})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (e^{2 x})

Apply the chain rule:

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

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

\frac{d}{d x} (2 x) = 2

= \frac{1}{2} e^{2 x} \cdot 2

Simplify

\frac{1}{2} e^{2 x} \cdot 2 : e^{2 x}

= e^{2 x}

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What is the derivative of 1/2 e^{2x} ?
The derivative of 1/2 e^{2x} is e^{2x}
What is the first derivative of 1/2 e^{2x} ?
The first derivative of 1/2 e^{2x} is e^{2x}