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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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