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Popular >

derivative of x/(1+e^x)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

Popular Examples

integral of (5x^2-3)/(x^3-x)

\int \frac{5 x ^{2} - 3}{x ^{3} - x} d x

tangent of f(x)=sin(pix^2)-pix,\at x=1 tangent of

f (x) = sin (π x^{2}) - π x, at x = 1

derivative of y=x^3-8x^2+21x+2 derivative of

y = x^{3} - 8 x^{2} + 21 x + 2

derivative of y=(90)/(x^5)derivative of

y = \frac{90}{x ^{5}}

2y^'-y=4asin(3t)

2 y^{^{'}} - y = 4 a sin (3 t)

Frequently Asked Questions (FAQ)

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