If y = (1 - x) ^2 x^2 , then dy dx is - Vidyadip

MCQ

If $y = {{{{(1 - x)}^2}} \over {{x^2}}}$, then ${{dy} \over {dx}}$ is

A
${2 \over {{x^2}}} + {2 \over {{x^3}}}$
B
$ - {2 \over {{x^2}}} + {2 \over {{x^3}}}$
C
$ - {2 \over {{x^2}}} - {2 \over {{x^3}}}$
✓
$ - {2 \over {{x^3}}} + {2 \over {{x^2}}}$

✓

Answer

Correct option: D.

$ - {2 \over {{x^3}}} + {2 \over {{x^2}}}$

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

$\Rightarrow \frac{{dy}}{{dx}} = - \frac{2}{{{x^3}}} + \frac{2}{{{x^2}}}$.

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