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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
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