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Popular >

derivative of sqrt(e^x+1)

Solution

\frac{d}{d x} (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

derivative of (arctan(x))^2 derivative of

(arctan (x))^{2}

(\partial)/(\partial x)(x^6)

\frac{\partial}{\partial x} (x^{6})

integral of ye^{-y/x}

\int y e^{- \frac{y}{x}} d y

integral from-infinity to 0 of 1/(6-2x)

\int_{- \infty}^{0} \frac{1}{6 - 2 x} d x

derivative of 3/(sqrt(1-x^2))

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

Frequently Asked Questions (FAQ)

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))