Find dy/dx: x² + xy + y² = 100

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 that x² + x y + y² = 100.

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

On differentiating with respect to x, we get

d/dx ( x² + x y + y²) = d/dx (100)

⇒ d/dx (x²) + d/dx (xy) + d/dx (y²) = 0 

Since derivative of constant function is zero.

⇒ 2x + [ y d/dx (x) + x dy/dx] + 2y dy/dx = 0

⇒ 2x + y + (x + 2y) dy/dx = 0

Therefore,

dy/dx = - (2x + y) / (x + 2y)

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

Find dy/dx: x² + x y + y² = 100

Summary:

The derivative of the given function x² + x y + y² = 100 is - (2x + y) / (x + 2y).A derivative helps us to know the changing relationship between two variables.