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Popular >

derivative of (1+e^x^{-2})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

= - \frac{2}{( 1 + e ^{x} ) ^{3}} e^{x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{2 e ^{x}}{( 1 + e ^{x} ) ^{3}}

Popular Examples

derivative of |x^3+10x^2+25x|

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

integral from 0 to 1 of x/(sqrt(4-x^2))

\int_{0}^{1} \frac{x}{4 - x ^{2}} d x

(d^2y)/(dx^2)+2(dy)/(dx)+5y=0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 5 y = 0

derivative of (sin^2(x)/(cos^2(x)))

\frac{d}{d x} (\frac{sin ^{2} ( x )}{cos ^{2} ( x )})

integral of x^a

\int x^{a} d x

Frequently Asked Questions (FAQ)

What is the derivative of (1+e^x^{-2}) ?
The derivative of (1+e^x^{-2}) is -(2e^x)/((1+e^x)^3)
What is the first derivative of (1+e^x^{-2}) ?
The first derivative of (1+e^x^{-2}) is -(2e^x)/((1+e^x)^3)