Question

Find the derivative of y with respect to x.

3y^2–6=x

Write your answer as a rational expression in one or both variables (x and y).


y′=

Answer 1

Explanation:

Here we have an implicit function, and so we must use implicit differentiation to find dy/dx.

(d/dx)(3y² - 6 = x) results in 6y(dy/dx) - 0 = (dx/dx), or 6y(dy/dx) = 1.

Then the desired derivative is

1

(dy/dx) = ---------

6y