Download App

5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = \sqrt {\sin x + y} ,$ then ${{dy} \over {dx}}$ equals to
  • A
    ${{\sin x} \over {2y - 1}}$
  • ✓
    ${{\cos x} \over {2y - 1}}$
  • C
    ${{\sin x} \over {2y + 1}}$
  • D
    ${{\cos x} \over {2y + 1}}$
✓

Answer

Correct option: B.
${{\cos x} \over {2y - 1}}$
b
(b) $y = \sqrt {\sin x + y} ,$ ==> ${y^2} = \sin x + y$

Differentiate with respect to $ x$ , 

$2y.\frac{{dy}}{{dx}} = \cos x + \frac{{dy}}{{dx}}$

==> $\frac{{dy}}{{dx}}(2y - 1) = \cos x$

==> $\frac{{dy}}{{dx}} = \frac{{\cos x}}{{2y - 1}}$.

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 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If the vectors  $a $ and $b$  are mutually perpendicular, then $a \times \{ a \times \{ a \times (a \times b)\} \} $ is equal to
→
If $\sin \left( {{{\sin }^{ - 1}}\frac{1}{5} + {{\cos }^{ - 1}}x} \right) = 1$, then $x$ is equal to
→
The domain of the function $f(x){ = ^{16 - x}}{\kern 1pt} {C_{2x - 1}}{ + ^{20 - 3x}}{\kern 1pt} {P_{4x - 5}}$, where the symbols have their usual meanings, is the set
→
Let $\mathrm{A}=\{1,2,3,4,5\}$. Let $\mathrm{R}$ be a relation on $\mathrm{A}$ defined by $x R y$ if and only if $4 x \leq 5 y$. Let $m$ be the number of elements in $\mathrm{R}$ and $\mathrm{n}$ be the minimum number of elements from $\mathrm{A} \times \mathrm{A}$ that are required to be added to $\mathrm{R}$ to make it a symmetric relation. Then $m+n$ is equal to:
→
If $f(x) = {1 \over {4{x^2} + 2x + 1}}$, then its maximum value is
→
Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability that both cards are queen is
→
The value of $\int\frac{\sin\text{x}+\cos\text{x}}{\sqrt{1-\sin2\text{x}}}\text{ dx}$ is equal to:
  1. $\sqrt{\sin2\text{x}}+\text{C}$
  2. $\sqrt{\cos2\text{x}}+\text{C}$
  3. $\pm(\sin\text{x}-\cos\text{x})+\text{C}$
  4. $\pm\log(\sin\text{x}-\cos\text{x})+\text{C}$
→
The optimal value of the objective function is attained at the points
→
A and B are two points and C is any point collinear with A and B. IF AB=10, BC=5, then AC is equal to:
  1. either 15 or 5
  2. necessarily 5
  3. necessarily 16
  4. none of these
→
Solve $\sin \left(\tan ^{-1} x\right),|x|<1$ is equal to
→