Continuity and Differentiability — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability2 Marks
Question
Find $\frac{d y}{d x}$, if $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$.
✓
Answer
Let x = a cos3 $\theta$, y = aSin3$\theta$ Then $\frac{d x}{d \theta}$ = -3a cos2 $\theta$ sin $\theta$ and $\frac{d y}{d \theta}$ = 3a sin2 $\theta$ cos $\theta$ Therefore, $\frac{d y}{d x}=\frac{\frac{d y}{d x}}{\frac{d x}{d \theta}}=\frac{3 a \sin ^{2} \theta \cos \theta}{-3 a \cos ^{2} \theta \sin \theta}=-\tan \theta=-\sqrt[3]{\frac{y}{x}}$
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