If {x^{2/3}} + {y^{2/3}} = {a^{2/3}},then fra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the equation: ${x^{2/3}} + {y^{2/3}} = {a^{2/3}}$Differentiating both sides with respect to $x$:$\frac{d}{dx}({x^{2/3}}) + \frac{d}{dx}({y^{

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Given the equation: ${x^{2/3}} + {y^{2/3}} = {a^{2/3}}$Differentiating both sides with respect to $x$:$\frac{d}{dx}({x^{2/3}}) + \frac{d}{dx}({y^{2/3}}) = \frac{d}{dx}({a^{2/3}})$Using the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$ and the chain rule for $y$:$\frac{2}{3}{x^{-1/3}} + \frac{2}{3}{y^{-1/3}}\frac{dy}{dx} = 0$Dividing by $\frac{2}{3}$:${x^{-1/3}} + {y^{-1/3}}\frac{dy}{dx} = 0$Rearranging to solve for $\frac{dy}{dx}$:${y^{-1/3}}\frac{dy}{dx} = -{x^{-1/3}}$$\frac{dy}{dx} = -\frac{{x^{-1/3}}}{{y^{-1/3}}}$$\frac{dy}{dx} = -{\left( \frac{x}{y} \right)^{-1/3}}$$\frac{dy}{dx} = -{\left( \frac{y}{x} \right)^{1/3}}$Thus,the correct option is $B$.

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

Similar Questions

$x\sqrt{1 + y} + y\sqrt{1 + x} = 0$,then $\frac{dy}{dx} = $

If $y = \frac{ax + b}{cx + d}$, then $\frac{dx}{dy} = $

If $(a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y)=a^2-b^2$ where $a>b>0$,then at $\left(\frac{\pi}{4}, \frac{\pi}{4}\right)$,$\frac{dy}{dx}=$

If $\sqrt[3]{y} \sqrt{x} = \sqrt[6]{(x+y)^{5}}$,then $\frac{dy}{dx} = $

If ${x^y} = {y^x},$ then $\frac{dy}{dx} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module