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

The derivative of f(x)=(x/(x^2+1))^2 is (2x(-x^2+1))/((x^2+1)^3)

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

The first derivative of f(x)=(x/(x^2+1))^2 is (2x(-x^2+1))/((x^2+1)^3)

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} + y = x e^{- x} + 1

n = 0 \sum \infty \frac{1}{n ( n + 2 )}

x \to 5 lim (x^{2} - 25)

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

\int_{0}^{1} \frac{4 x + 6}{( x + 1 ) ^{2}} d x

What is the derivative of f(x)=(x/(x^2+1))^2 ?
The derivative of f(x)=(x/(x^2+1))^2 is (2x(-x^2+1))/((x^2+1)^3)
What is the first derivative of f(x)=(x/(x^2+1))^2 ?
The first derivative of f(x)=(x/(x^2+1))^2 is (2x(-x^2+1))/((x^2+1)^3)