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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x^{2} y^{^{''}} + 9 x y^{^{'}} + 16 y = 0

f (x) = sin (5 x)

x \to - 3 lim (- x^{2} + 6 x - 2)

\int 54.0595 e^{x} x d x

\frac{\partial}{\partial x} (in \frac{x + y}{x - y})

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