Question

Y is a differentiable function of x. Choose the alternative that is the derivative dy / dx.


`x^3-y^3=1`

a)
`x`
b)
`3x^2`
c)
`√(3x^2)`
d)
`x^2 / y^2`
e)
`(3x^2-1)/(y^2)`

Answer 1

Differentiating both sides of

`x^3-y^3=1`

with respect to x yields (using the chain rule)

`3x^2 - 3y^2 (\mathrm dy)/(\mathrm dx) = 0`

Solve for dy/dx :

`3x^2 - 3y^2 (\mathrm dy)/(\mathrm dx) = 0 \\\\ 3y^2(\mathrm dy)/(\mathrm dx) = 3x^2 \\\\ (\mathrm dy)/(\mathrm dx) = (3x^2)/(3y^2) = (x^2)/(y^2)`

The answer is then D.