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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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