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

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 x

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

On differentiating with respect to x, we get

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

⇒ d/dx(2x) + d/dx(3y)

= cos x

⇒ 2 + 3dy/dx = cos x

[ d/dx (2x) = 2 and d/dx (sin x) = cos x ]

⇒ 3 dy/dx = cos x − 2 [ transposing the terms]

Therefore,

dy/dx = (cos x − 2) / 3

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NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.3 Question 1

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

Summary:

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