If √(1 - x^6) + √(1 - y^6) = a^3(x^3 - y^3), then dy/dx is equal to A. x^2/y^2 √((1 - y^6)/(1 - x^6))

Question

If \(\sqrt{1-\text x^6}+\sqrt{1-y^6}\) =  a³(x³ - y³), then \(\cfrac{dy}{d\mathrm x} \) is equal to

A. \(\cfrac{\text x^2}{y^2}\sqrt{\cfrac{1-y^6}{1-\text x^6}}\)

B. \(\cfrac{y^2}{\text x^2}\sqrt{\cfrac{1-y^6}{1-\text x^6}}\)

C. \(\cfrac{\text x^2}{y^2}\sqrt{\cfrac{1-\text x^6}{1- y^6}}\) 

D. none of these

Answer 1

Correct option is  A. \(\cfrac{\text x^2}{y^2}\sqrt{\cfrac{1-y^6}{1-\text x^6}}\) 

\(\sqrt{1-\text x^6}+\sqrt{1-y^6}\) = a³(x³ - y³)

Let x³ = cos p and y³ = cos q

cos^-1x³ = p and cos^-1y³ = q --- (1)

Comparing L.H.S and R.H.S we get

⇒ \(\cfrac{dy}{d\mathrm x} \) = \(\cfrac{\text x^2}{y^2}\sqrt{\cfrac{1-y^6}{1-\text x^6}}\)