If (cos x)^ y =(cos y)^ x ,find dy dx . - Vidyadip

Question

$\text{If (cos x)}^{\text{y}}=\text{(cos y)}^{\text{x}},\text{find }\frac{\text{dy}}{\text{dx}}.$

✓

Answer

$\text{(cos x)}^{\text{y}}=\text{(cos y)}^{\text{x}}\Rightarrow$ y log cos x = x log cos y.$\therefore\text{y}.\frac{\text{(-sin x)}}{\text{cos x}}+\text{log cos x.}\frac{\text{dy}}{\text{dx}}=\text{x}.\frac{\text{(-sin y)}}{\text{cos y}}\frac{\text{dy}}{\text{dx}}+\text{log cos y.}$
(log cos x + x tan y) $\frac{\text{dy}}{\text{dx}}$ = log cos y + y tan x
$\therefore\frac{\text{dy}}{\text{dx}}= \frac{\text{log cos y + y tan x}}{\text{log cos x + x tan y}}$.

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 "5 Marks Questions" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Differentiate the following functions from first principles:
$\log\cos\text{x}$

At every point on a curve the slope is the sum of the abscissa and the product of the ordinate and the abscissa, and the curve passes through (0, 1). Find the equation of the curve.

Solve the following differential equations:$(1+\text{x})(1+\text{y}^2)\text{dx}+(1+\text{y})(1+\text{x}^2)\text{dy}=0$

On Z, the set of all integers, a binary operation * is defined by a * b = a + 3b - 4. Prove that * is neither commutative nor associative on Z.

If $\text{x}=\text{a}\Big(\frac{1+\text{t}^2}{1-\text{t}^2}\Big)\text{ and y}=\frac{2\text{t}}{1-\text{t}^2},$ find $\frac{\text{dy}}{\text{dx}}$

Evaluate the following integrals:$\int\frac{5\text{x}-2}{1+2\text{x}+3\text{x}^2}\text{ dx}$

$\text{Find:}\int \frac{\text{x}\ \text{dx}}{(2 + \text{x}^{\text{2}}) (4 + \text{e}^{4\text{}})}$

Evaluate the following integrals as limit of sum:
$\int\limits^{2}_{0}\big(\text{x}^2+2\text{x}+1\big)\text{dx}$

A manufacturer can produce two products, A and B, during a given time period. Each of these products requires four different manufacturing operations: grinding, turning, assembling and testing. The manufacturing requirements in hours per unit of products A and B are given below.

	A	B
Grinding	1	2
Turning	3	1
Assembling	6	3
Testing	5	4

The available capacities of these operations in hours for the given time period are: grinding 30; turning 60, assembling 200; testing 200. The contribution to profit is Rs 20 for each unit of A and Rs 30 for each unit of B. The firm can sell all that it produces at the prevailing market price. Determine the optimum amount of A and B to produce during the given time period. Formulate this as a LPP.

Using integration, find the area of the region bounded by the triangle whose vertices are (–1, 2), (1, 5) and (3, 4).