NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

If log 10 ⁡ x 3 - y 3 x 3 + y 3 = 2 , then d y d x =

Options

Ax y
B- y x
C- x y
Dy x

Correct answer

D. y x

Step-by-step solution

Given, log 10 ⁡ x 3 - y 3 x 3 + y 3 = 2 ⇒ x 3 - y 3 x 3 + y 3 = 10 2 = 100 Applying componendo and dividendo, we get, x 3 y 3 = - 101 99 ⇒ x y = - 101 99 1 3 ......(i) Hence, y = - 99 101 1 3 x Differentiating, we get, d y d x = - 99 101 1 3 = y x (from (i))

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