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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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\frac{d}{d x} (\frac{3}{1 - x ^{2}})

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