Find dy/dx: xy + y² = tan x + y

Solution:

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

The change in the value of the dependent variable with respect to the change in the value of the independent variable expression can be found using the derivative formula.

Given, x y + y² = tan x + y

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

On differentiating with respect to x, we get

d/dx (x y + y²) = d/dx(tan x + y)

⇒d/dx(x y) + d/dx(y²) = d/dx (tan x) + dy/dx

⇒[y.d/dx(x) + x.dy/dx] + 2y dy/dx

= sec²x + 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.

⇒y.1+x dy/dx + 2y dy/dx

= sec²x + dy/dx

⇒ (x + 2y −1) dy/dx = sec²x − y

Therefore,

dy/dx = (sec²x − y) / (x + 2y −1)

NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.3 Question 4