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Popular >

derivative of f(-x)= x/(x^2+1)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

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

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

Graph

Popular Examples

integral of 1/(sqrt(x^2-361))

\int \frac{1}{x ^{2} - 361} d x

limit as x approaches 0 of x/(-3x^3+2)

x \to 0 lim (\frac{x}{- 3 x ^{3} + 2})

limit as x approaches infinity of e^{-x}

x \to \infty lim (e^{- x})

integral of (sqrt(x^3)+\sqrt[3]{x^2})

\int (x^{3} + 3 x^{2}) d x

integral of ((ln(x))^{15})/x

\int \frac{( ln ( x ) ) ^{15}}{x} d x

Frequently Asked Questions (FAQ)

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