# Find dy/dx: ax + by^{2} = cosy

**Solution:**

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

Given,

ax + by^{2} = cos y

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

On differentiating with respect to x, we get

d/dx (ax) + d/dx (by^{2}) = d/dx (cosy)

[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.

⇒ a + b d/dx (y^{2}) = d/dx (cosy) …(1)

d/dx (y^{2}) = 2y dy/dx

and d/dx (cos y) = −sin y dy/dx …(2)

From (1) and (2), we obtain

a + b × 2y dy/dx = −siny dy/dx

⇒ (2by + siny) dy/dx = −a

Therefore,

dy/dx = −a/(2by + sin y)

NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.3 Question 3

## Find dy/dx: ax + by^{2} = cosy

**Summary:**

The derivative of ax + by^{2} = cosy with respect to x is dy/dx = −a/(2by + sin y) .A derivative helps us to know the changing relationship between two variables

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