Find d y d x , if x^ 2 3 +y^ 2 3 =a^ 2 3 . - Vidyadip

Question

Find $\frac{d y}{d x}$, if $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$.

✓

Answer

Let $x = a \cos^3 \theta, y = a\ Sin^3 \theta$
Then $\frac{d x}{d \theta} = -3a \cos^2 \theta$ sin $\theta$
and $\frac{d y}{d \theta} = 3a \sin^2 \theta$ cos $\theta$
Therefore, $\frac{d y}{d x}=\frac{\frac{d y}{d x}}{\frac{d x}{d \theta}}=\frac{3 a \sin ^{2} \theta \cos \theta}{-3 a \cos ^{2} \theta \sin \theta}=-\tan \theta=-\sqrt[3]{\frac{y}{x}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Continuity and Differentiability→Continuity and Differentiability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find a unit vector perpendicular to vectors $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$, when $\vec{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}+2 \hat{k}$

Evaluate the following:
$\sin^{-1}(\sin2)$

A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its cooler is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be,
Blue and red in any order.

Given that $\vec{a} \cdot \vec{b}=0$ and $\vec{a} \times \vec{b}=\overrightarrow{0}$. What can you conclude about the vectors $\vec a $ and $\vec b$?

Integrate the function $\frac{3 x^{2}}{x^{6}+1}$

If $\vec{\text{c}}$ is a unit vector perpendicular to the vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ write another unit vector perpendicular to $\vec{\text{a}}$ and $\vec{\text{b}}.$

Let $A = [a_{ij}]$ be a square matrix of order $3 \times 3$ and $C_{ij}$ denote cofactor of $a_{ij}$ in $A.$ if $|A| = 5,$ write the value of $a_{13}C_{13} + a_{23}C_{23} + a_{33}C_{33.}$

Find $\vec{\text{a}}.\vec{\text{b}}$ when
$\vec{\text{a}}=\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{k}}$

Let $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix}$ and $\text{C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}.$ Find each of the following:
$3\text{A}-\text{C}$

Evaluate the following definite integrals:
$\int_{0}^\limits{1}\frac{1}{1+\text{x}^2} \text{ dx}$