Question

If `y = sin^-1(1/x^3)`, then `dy/dx` = ______ 

विकल्प

• `-3/(x^4 sin[cos^-1(1/x^3)])`

• `3/(xsqrt(x^6 - 1))`

• `3/(x^4 sin[cos^-1(1/x^3)])`

• `(-3)/(xsqrt(x^6 - 1))`

Answer 1

If `y = sin^-1(1/x^3)`, then `dy/dx` = `underline((-3)/(xsqrt(x^6 - 1)))`

Explanation:

`y = sin^-1(1/x^3)`

∴ `y = cosec^-1(x^3)`

∴ `dy/dx = (-1)/(x^3sqrt((x^3)^2 - 1)) . 3x^2 = (-3)/(xsqrt(x^6 - 1))`