$$ y ^ { \prime } = ( \frac { x - 1 } { x ^ { 2 } } ) ^ { \prime } $$

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It seems that the calculation for the derivative of $$x^2$$ is not supported. Let's calculate it manually.

The derivative of $$x^2$$ with respect to $$x$$ is $$2x$$.

Now, we can apply the quotient rule to find the derivative of $$(x-1)/(x^2)$$. According to the quotient rule:

$$
\frac{d}{dx}\left(\frac{x-1}{x^2}\right) = \frac{(1)(x^2) - (x-1)(2x)}{(x^2)^2}
$$

Simplifying this expression will give us the derivative of $$(x-1)/(x^2)$$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(1\times x^{2}-\left(x-1\right)\times 2x\right)}{\left(x^{2}\right)^{2}}$$
- step1: Remove the parentheses:
  $$\frac{1\times x^{2}-\left(x-1\right)\times 2x}{\left(x^{2}\right)^{2}}$$
- step2: Multiply the exponents:
  $$\frac{1\times x^{2}-\left(x-1\right)\times 2x}{x^{2\times 2}}$$
- step3: Multiply:
  $$\frac{x^{2}-\left(x-1\right)\times 2x}{x^{2\times 2}}$$
- step4: Multiply the terms:
  $$\frac{x^{2}+2x\left(-x+1\right)}{x^{2\times 2}}$$
- step5: Multiply the numbers:
  $$\frac{x^{2}+2x\left(-x+1\right)}{x^{4}}$$
- step6: Add the terms:
  $$\frac{-x^{2}+2x}{x^{4}}$$
- step7: Factor the expression:
  $$\frac{x\left(-x+2\right)}{x^{4}}$$
- step8: Reduce the fraction:
  $$\frac{-x+2}{x^{3}}$$
The derivative of $$(x-1)/(x^2)$$ is $$\frac{-x+2}{x^3}$$.

Therefore, $$y' = \frac{-x+2}{x^3}$$.
Дериватив функции $$ \frac{x-1}{x^2} $$ равен $$ \frac{-x+2}{x^3} $$.

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

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