Implicit Differentiation Solver

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Implicit derivative is the special form of chain rule derivative where we can differentiate an implicit equation with the help of chain rule differentiation.

Question 1: - If 2 x ^2 + 3 y ^2 = 9, find dy/dx.

Solution: - 2 x ^2 + 3 y ^2 = 9

Differentiating both sides w.r.t. x,

2 d/dx (x ^2) + 3 d/dx (y ^2) = d/dx (9)

2 * 2x + 3 (2y) dy/dx = 0

6 y dy/dx = - 4 x

dy/dx = -4 x / 6 y

dy/dx = -2 x / 3 y

Therefore dy/dx = -2x / 3y

Question 2: - If 8 x^2 + 2 x y + 9 x^2 = 20, find dy / dx.

Solution: - 8 x^2 + 2 x y + 9 x^2 = 20

Differentiating both sides w.r.t. x,

8 d/dx (x ^2) + 2 d/dx (x y) + 9 d/dx (x ^2) = d/dx (20)

8 (2 x) + 2 {y d/dx (x) + x d /dx (y)} + 9 *2 x = 0

16 x + 2 (y * 1 + x dy /dx) + 18 x = 0

16 x + 2 y + 2 x dy /dx = 0

2 x dy /dx = - 16 x – 2 y

2 x dy / dx = - 2 (8 x + y)

x dy / dx = - (8 x + y)

dy / d x = - (8 x + y) / x

 
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