Find dy dx , when x=b ^2 and y=a ^2 - Vidyadip

Question

Find $\frac{\text{dy}}{\text{dx}},$ when
$\text{x}=\text{b}\sin^2\theta\text{ and y}=\text{a}\cos^2\theta$

✓

Answer

Here $\text{x}=\text{b}\sin^2\theta\text{ and y}=\text{a}\cos^2\theta$Then,
$\frac{\text{dx}}{\text{d}\theta}=\frac{\text{d}}{\text{d}\theta}(\text{b}\sin^2\theta)=2\text{b}\sin\theta\cos\theta$
$\frac{\text{dy}}{\text{d}\theta}=\frac{\text{d}}{\text{d}\theta}(\text{a}\cos^2\theta)=2\text{b}\cos\theta\sin\theta$
$\therefore\frac{\text{dy}}{\text{d}\text{x}}=\frac{\frac{\text{dy}}{\text{d}\theta}}{\frac{\text{dx}}{\text{d}\theta}}=\frac{-2\text{a}\cos\theta\sin\theta}{2\text{b}\sin\theta\cos\theta}=\frac{-\text{a}}{\text{b}}$

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 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

Differentiate the $\sqrt{e^{\sqrt{x}}}, x>0$ w.r.t. x.

Find the cosine of the angle between the vectors $4\hat{\text{i}}-3\hat{\text{j}}+3\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}-\hat{\text{k}}.$

Find the particular solution of the differential equation $\frac{d y}{d x} = -4xy^2$ given that $y = 1$, when $x = 0$

If f(x) attains a local minimum at x = c, then write the values of f' (c) and f'' (c).

If $I_3$ denotes identity matrix of order $3 \times 3$, write the value of its determinant.

Let A and B be square matrices of the same order. Does $(A + B)^2 = A^2 + 2AB + B^2$ hold? If not, why?

Determine whether or not the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation give justification of this.
On $R$, define $*$ by $a * b = a + 4b^2$
Here, $Z^+$ denotes the set of all non-negative integers.

A random variable X has the following probability distribution:

Values of X:	0	1	2	3	4	5	6	7	8
P(X)	a	3a	5a	7a	9a	11a	13a	15a	17a

Determine:
The Value of a.

Evaluate the following:
$\big[\hat{\text{i}}\hat{\text{j}}\hat{\text{k}}\big]+\big[\hat{\text{j}}\hat{\text{k}}\hat{\text{i}}\big]+\big[\hat{\text{k}}\hat{\text{i}}\hat{\text{j}}\big]$

Find the equation of the plane passing through the following point:
(0, -1, 0), (3, 3, 0) and (1, 1, 1)