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

The derivative of ((2x/(x^2+1))^2) is (8x(-x^2+1))/((x^2+1)^3)

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

The first derivative of ((2x/(x^2+1))^2) is (8x(-x^2+1))/((x^2+1)^3)

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

\frac{8 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 \cdot \frac{2 x}{x ^{2} + 1} \cdot \frac{2 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}} : \frac{8 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

= \frac{8 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

\frac{\partial}{\partial y} (e^{- y} cos (x))

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

\frac{d}{d x} (2 x^{3} ln (3 x - 2))

\frac{\partial}{\partial y} (- 5 y^{6} sin (5 x))

\frac{d}{d x} (50 (80 - x)^{2})

What is the derivative of ((2x/(x^2+1))^2) ?
The derivative of ((2x/(x^2+1))^2) is (8x(-x^2+1))/((x^2+1)^3)
What is the first derivative of ((2x/(x^2+1))^2) ?
The first derivative of ((2x/(x^2+1))^2) is (8x(-x^2+1))/((x^2+1)^3)