What is the derivative of sqrt(e^{2x)} ?

The derivative of sqrt(e^{2x)} is e^x

What is the first derivative of sqrt(e^{2x)} ?

The first derivative of sqrt(e^{2x)} is e^x

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

e^{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= e^{x}

What is the derivative of sqrt(e^{2x)} ?
The derivative of sqrt(e^{2x)} is e^x
What is the first derivative of sqrt(e^{2x)} ?
The first derivative of sqrt(e^{2x)} is e^x