Find dy/dx: 2x + 3y = siny

Solution:

A derivative helps us to know the changing relationship between two variables. Consider the independent variable 'x' and the dependent variable 'y'.

Given,

2x + 3y = sin y

Let us find the derivative on both sides with respect to x.

On differentiating with respect to x, we get

d/dx (2x) + d/dx (3y) = d/dx (sin y)

⇒ 2 + 3dy/dx = cosy dy/dx

[By using chain rule of derivative]

i.e we need to differentiate all the functions present in the problem separately and then multiply at the end.

⇒ 2 = (cos y−3) dy/dx

Therefore,

dy/dx = 2 / (cos y−3)

NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.3 Question 2

Find dy/dx: 2x + 3y = siny

Summary:

The derivative of  2x + 3y = sin y with respect to x is dy/dx = (cos y − 3) /2. A derivative helps us to know the changing relationship between two variables