What is the derivative of sqrt(1+e^{2x)} ?

The derivative of sqrt(1+e^{2x)} is (e^{2x})/(sqrt(1+e^{2x))}

What is the first derivative of sqrt(1+e^{2x)} ?

The first derivative of sqrt(1+e^{2x)} is (e^{2x})/(sqrt(1+e^{2x))}

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derivative of

1 + e^{2 x}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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