Download App

Differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferentiation3 Marks
Question
Find $\frac{\text{dy}}{\text{dx}}$ in the following cases:
$\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$
✓

Answer

Given,
$\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$
Differentiating with resepct to x,
$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}\Big)=\frac{\text{d}}{\text{dx}}(1)$
$\Rightarrow\frac{\text{d}}{\text{dx}}\Big(\frac{\text{x}^2}{\text{a}^2}\Big)+\frac{\text{d}}{\text{dx}}\Big(\frac{\text{y}^2}{\text{b}^2}\Big)=0$
$\Rightarrow\frac{1}{\text{a}^2}(2{\text{x}})+\frac{1}{\text{b}^2}(2\text{y})\frac{\text{d}}{\text{dx}}=0$
$\Rightarrow\frac{2\text{y}}{\text{b}^2}\frac{\text{dy}}{\text{dx}}=-\frac{2{\text{x}}}{\text{a}^2}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=-\Big(\frac{2{\text{x}}}{\text{a}^2}\Big)\Big(\frac{\text{b}^2}{2\text{y}}\Big)$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=-\frac{{\text{b}^2\text{x}}}{\text{a}^2\text{y}}$

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 "3 Marks Question" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write the value of $\cos^{-1}\Big(\tan\frac{3\pi}{4}\Big).$
→
Differentiate the following functions with respect to x:
$2^{\text{x}^3}$
→
If $\big|\vec{\text{a}}\times\vec{\text{b}}\big|^2+\big|\vec{\text{a}}.\vec{\text{b}}\big|^2=400$ and $|\vec{\text{a}}|=5,$ then write the value of $\big|\vec{\text{b}}\big|.$
→
Show that the Lagrange's mean value theorem is not applicable to the function
$\text{f}(\text{x})=\frac{1}{\text{x}}\text{ on }[-1,1]$
→
Prove that the function $f$ given by $f(x) = x - [x]$ is increasing in $(0, 1).$
→
A fair die is rolled. Consider events E = $\{1,\ 3,\ 5\},\ \text{F}=\{2,\ 3\}\ \text{and}\ \text{G}=\{2,\ 3,\ 4,\ 5\}.\ \text{Find}:$ $\text{P}\Big[(\text{E}\cup\text{F})|\text{G}\Big]\ \text{and}\ \text{P}\Big[(\text{E}\cap\text{F})|\text{G}\Big]$
→
Evaluate $\sin\Big(\tan^{-1}\frac{3}{4}\Big).$
→
Write the minors and cofactors of element of the first column of the following matrices and hence evaluate the determinant in case:
$\text{A}=\begin{vmatrix}-1&4\\2&3 \end{vmatrix}$
→
If $\vec{\text{a}}=3\hat{\text{i}}-\hat{\text{j}}-2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+3\hat{\text{j}}+\hat{\text{k}},$ find $\big(\vec{\text{a}}+2\vec{\text{b}}\big)\times\big(\vec{\text{a}}-2\vec{\text{b}}\big).$
→
Evaluate the following integrals:
$\int\frac{1}{\text{x}^{\frac{3}{2}}}\text{dx}$
→