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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{2} + 1}) = \frac{4 x}{( x ^{2} + 1 ) ^{2}}

= 2 \cdot \frac{x ^{2} - 1}{x ^{2} + 1} \cdot \frac{4 x}{( x ^{2} + 1 ) ^{2}}

Simplify

2 \cdot \frac{x ^{2} - 1}{x ^{2} + 1} \cdot \frac{4 x}{( x ^{2} + 1 ) ^{2}} : \frac{8 x ( x ^{2} - 1 )}{( x ^{2} + 1 ) ^{3}}

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

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