If x^ 2/3 + y^ 2/3 = a^ 2/3 , then dy dx = - Vidyadip

MCQ

If ${x^{2/3}} + {y^{2/3}} = {a^{2/3}}$, then ${{dy} \over {dx}} = $

A
${\left( {{y \over x}} \right)^{1/3}}$
✓
$ - {\left( {{y \over x}} \right)^{1/3}}$
C
${\left( {{x \over y}} \right)^{1/3}}$
D
$ - {\left( {{x \over y}} \right)^{1/3}}$

✓

Answer

Correct option: B.

$ - {\left( {{y \over x}} \right)^{1/3}}$

b
(b) ${x^{2/3}} + {y^{2/3}} = {a^{2/3}}$

==> $\frac{2}{3}{x^{ - 1/3}} + \frac{2}{3}{y^{ - 1/3}}\frac{{dy}}{{dx}} = 0$ or

$\frac{{dy}}{{dx}} = - {\left( {\frac{x}{y}} \right)^{ - 1/3}} = - {\left( {\frac{y}{x}} \right)^{1/3}}$.

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