Download App

Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
Let $\text{y}=\sqrt{\sin\text{x}+\text{y}},$ then $\frac{\text{dy}}{\text{dx}}=$
  • A
    $\frac{\sin\text{x}}{2\text{y}-1}$
  • B
    $\frac{\sin\text{x}}{1-2\text{y}}$
  • C
    $\frac{\cos\text{x}}{1-2\text{y}}$
  • ✓
    $\frac{\cos\text{x}}{2\text{y}-1}$
✓

Answer

Correct option: D.
$\frac{\cos\text{x}}{2\text{y}-1}$
$\text{y}=\sqrt{\sin\text{x}+\text{y}}$
$\frac{\text{dy}}{\text{dx}}=\frac{1}{2\sqrt{\sin\text{x}+\text{y}}}\times\Big(\cos\text{x}+\frac{\text{dy}}{\text{dx}}\Big)$
$\frac{\text{dy}}{\text{dx}}=\frac{\cos\text{x}}{2\sqrt{\sin\text{x}+\text{y}}}+\frac{1}{2\sqrt{\sin\text{x}+\text{y}}}\frac{\text{dy}}{\text{dx}}$
$\frac{\text{dy}}{\text{dx}}-\frac{1}{2\sqrt{\sin\text{x}+\text{y}}}\frac{\text{dy}}{\text{dx}}=\frac{\cos\text{x}}{2\sqrt{\sin\text{x}+\text{y}}}$
$\Big(1-\frac{1}{2\sqrt{\sin\text{x}+\text{y}}}\Big)\frac{\text{dy}}{\text{dx}}=\frac{\cos\text{x}}{2\sqrt{\sin\text{x}+\text{y}}}$
$\Big(1-\frac{1}{2\text{y}}\Big)\frac{\text{dy}}{\text{dx}}=\frac{\cos\text{x}}{2\text{y}}$
$\Big(\frac{2\text{y}-1}{2\text{y}}\Big)\frac{\text{dy}}{\text{dx}}=\frac{\cos\text{x}}{2\text{y}}$
$\frac{\text{dy}}{\text{dx}}=\frac{\cos\text{x}}{2\text{y}-1}$

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 "M.C.Q (1 Marks)" 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

$\int\frac{\text{a}}{(1+\text{x}^2)\tan^{-1}\text{x}}\text{dx}=$
→
if $\text{y}=\text{e}^{{\tan}\text{x}},$ then $(\cos^2\text{x})\text{y}_2=$
→
The function $x + {1 \over x},(x \ne 0)$ is a non-increasing function in the interval
→
$\int {{{\sec }^2}\theta } \,\,{(\sec \theta \, + \,\tan \theta )^2}\,\,d\theta $
→
$\int_{\pi /3}^{\pi /2} {\frac{{\sqrt {1 + \cos x} }}{{{{(1 - \cos x)}^{\frac{5}{2}}}}}} \,dx = $
→
Choose the correct answer in Exercise : The value of $\int^{\frac{\pi}{2}}\limits_{0}\log\bigg(\frac{4+3\sin\text{x}}{4+3\cos\text{x}}\bigg)\text{dx}\ $is
→
If $y = ax^2 + b,$ then $\frac{\text{dy}}{\text{dx}}$ at $x = 2$ is equal to:
→
One ticket is drawn from a bag containing $70$ tickets numbered $1$ to $70$ Find the probability that it is a multiple of $5$ or $7$ :
→
$\int {\frac{{(2x + 1)}}{{{{({x^2}\, + 4x + 1)}^{\frac{3}{2}}}}}\,\,dx} $
→
If the value of the integral $\int \limits_{0}^{\frac{1}{2}} \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x$ is $\frac{ k }{6},$ then $k$ is equal to
→