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Popular >

derivative of y=sqrt(e^x+1)

Solution

derivative of

y = e^{x} + 1

Solution

\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}

Popular Examples

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\frac{d}{d x} (- 2 sin (2 x) + 2 cos (2 x))

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\frac{x}{x - 8}

limit as x approaches 0+of 2xe^{-3x}

x \to 0 + lim (2 x e^{- 3 x})

integral from 0 to 16 of (500x)/(x^2+24)

\int_{0}^{16} \frac{500 x}{x ^{2} + 24} d x

derivative of 5pix^2 derivative of

5 π x^{2}

Frequently Asked Questions (FAQ)

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