Download App

CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
Find $\frac{\text{dx}}{{\text{dy}}}$ in the following:
$\text{ax} + \text{by}^{2} = \cos\text{y}$
✓

Answer

The given relationship is $\text{ax} + \text{by}^{2} = \cos\text{y}$
Differentiating this relationship with respect to x, we obtain
$\frac{\text{d}}{\text{dx}}(\text{ax}) + \frac{\text{d}}{\text{dx}}(\text{by}^{2}) =\frac{\text{d}}{\text{dx}}( \cos\text{y})$
$\Rightarrow \text{a + b}\frac{\text{d}}{\text{dx}}(\text{y}^{2}) =\frac{\text{d}}{\text{dx}}( \cos\text{y}) ...(\text{i})$
Using chain rule, we obtain $\frac{\text{d}}{\text{dx}}(\text{y}^{2}) = 2\text{y}\frac{\text{dy}}{\text{dx}}\ \text{and}\ \frac{\text{d}}{\text{dx}}( \cos\text{y}) = -\sin\text{y}\frac{\text{dy}}{\text{dx}} ...{\text{(ii)}}$
Form (i) and (ii), we obtain
$\text{a + b}\times 2\text{y}\frac{\text{dy}}{\text{dx}} = -\sin\text{y}\frac{\text{dy}}{\text{dx}}$
$\Rightarrow(2\text{by} + \sin\text{y})\frac{\text{dy}}{\text{dx}} = -\text{a}$
$\therefore\frac{\text{dy}}{\text{dx}} =\frac{\text{-a}}{2\text{by} + \sin\text{y}}$

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 "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

A ladder $13 m$ long is leaning against a vertical wall. The bottom of the ladder is dragged away from the wall along the ground at the rate of $2 \ cm/\sec.$ How fast is the height on the wall decreasing when the foot of the ladder is $5 m$ away from the wall?
→
Evaluate the following integrals:
$\int\frac{1}{1+\text{x}-\text{x}^2}\text{dx}$
→
Find the maximum and minimum value of, h(x) = sin(2x) + 5
→
What are the direction cosines of X-axis?
→
Find the magnitude of two vectors $\vec a$ and $\vec b$, having the same magnitude and such that the angle between them is $60^\circ$ and their scalar product is $\frac{1}{2}$.
→
Integrate the functions in Exercises:
$\frac{3\text{x}^2}{\text{x}^6+1}$
→
Determine the direction cosines of the normal to the plane and the distance from the origin.
2x + 3y - z = 5
→
Integrate the function in Exercise:$\cos^{3}\text{x}\ \text{e}^{\log\sin\text{x}}$
→
A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that.
none of the bulbs is defective.
→
Let C be the set of complex numbers. Prove that the mapping f : C → R given by f(z) = |z|, ∀ z ∈ C, is neither one-one nor onto.
→