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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

\int_{1}^{4} \frac{x ^{2} + 3}{5 x - x ^{2}} d x

n = 1 \sum \infty n n

f (x) = tan (\frac{3 π}{4} x)

\int a^{- x} d x

x \to 3 - lim (arcsin (\frac{x}{3}))

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