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

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

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

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

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derivative of

(\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}}

\frac{4 ln ( x + 2 )}{x ^{2}}

f (x) = 2 x^{3} - 5 x^{2} + 10 x + 2

\frac{1}{( x + 1 )}

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

y = (1 0^{x})^{2}

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