Download App

Differentiation — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiation5 Marks
Question
Find $\frac{\text{dy}}{\text{dx}}$ in the following cases:
$4\text{x}+3\text{y}=\log\big(4\text{x}-3\text{y}\big)$
✓

Answer

We have, $4\text{x}+3\text{y}=\log\big(4\text{x}-3\text{y}\big)$
Differentiating with respect to x, we get,
$\frac{\text{d}}{\text{dx}}\big(4\text{x}\big)+\frac{\text{d}}{\text{dx}}\big(3\text{y}\big)=\frac{\text{d}}{\text{dx}}\big\{\log\big(4\text{x}-3\text{y}\big)\big\}$
$\Rightarrow4+3\frac{\text{dy}}{\text{dx}}=\frac{1}{\big(4\text{x}-3\text{y}\big)}\frac{\text{d}}{\text{dx}}\big(4\text{x}-3\text{y}\big)$
$\Rightarrow4+3\frac{\text{dy}}{\text{dx}}=\frac{1}{\big(4\text{x}-3\text{y}\big)}\Big(4-3\frac{\text{dy}}{\text{dx}}\Big)$
$\Rightarrow3\frac{\text{dy}}{\text{dx}}+\frac{3}{\big(4\text{x}-3\text{y}\big)}\frac{\text{dy}}{\text{dx}}=\frac{4}{\big(4\text{x}-3\text{y}\big)}-4$
$\Rightarrow3\frac{\text{dy}}{\text{dx}}\Big\{1+\frac{1}{(4\text{x}-3\text{y})}\Big\}=4\Big\{\frac{1}{(4\text{x}-3\text{y})}-1\Big\}$
$\Rightarrow3\frac{\text{dy}}{\text{dx}}\Big\{\frac{4\text{x}-3\text{y}+1}{(4\text{x}+3\text{y})}\Big\}=4\Big\{\frac{1-4\text{x}-3\text{y}}{4\text{x}-3\text{y}}\Big\}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{4}{3}\Big\{\frac{1-4\text{x}+3\text{y}}{(4\text{x}-3\text{y})}\Big\}\Big(\frac{4\text{x}-3\text{y}}{4\text{x}-3\text{y}+1}\Big)$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{4}{3}\Big(\frac{1-4\text{x}+3\text{y}}{4\text{x}-3\text{y}+1}\Big)$

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 "Solve the Following Question.(5 Marks)" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate the following integrals:$\int_{0}^\limits{\frac{\pi}{2}}\frac{\sin\text{x}\cos\text{x}}{1+\sin^4\text{x}}\text{ dx}$
→
Evaluate the following integrals:$\int\text{e}^{\text{x}}\Big(\frac{\sin4\text{x}-4}{1-\cos4\text{x}}\Big)\text{dx}$
→
Find the equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0.
→
Solve the following systems of linear equations by cramer's rule:
2x - y = 1,
7x - 2y = -7
→
Find the feasible solution of the following inequations graphically.0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x + y ≤ 5, 2x + y ≥ 4
→
Write the minimum value of$ f(x) = x^x .$
→
Represent the following families of curves by forming the corresponding differential equation:
$\frac{\text{x}^2}{\text{a}^2}-\frac{\text{y}^2}{\text{b}^2}=1$
→
Prove that the given vectors are non-coplanar:
$3\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}},\ 2\hat{\text{i}}-\hat{\text{j}}+7\hat{\text{k}}$ and $7\hat{\text{i}}-\hat{\text{j}}+23\hat{\text{k}}$
→
Find the equation of the plane that contains the point (1, -1, 2) and is perpendicular to each of the planes 2x + 3y - 2z = 5 and x + 2y - 3z = 8.
→
Evaluate :

$\int \frac{3 x+4}{\sqrt{2 x^2+2 x+1}} d x$

→