well this week we learned about implicit derivatives. an implicit derivative is when you take a derivative with respect to another variable. for example, dy/dx would stand for the derivative of y with respect to the variable, x.

for example: 2y^2 - x^2 + 8x = 7

dy/dx[f(x)] = 4y - 2x + 8

you would then set dy/dx as a coefficient to y in order to solve for the implicit derivative.

(4y)(dy/dx) - 2x +8 = 0

all you do now is solve for dy/dx.

(4y)(dy/dx) - 2x = -8

4y(dy/dx) = 2x - 8

dy/dx = (2x - 8) / 4y

dy/dx = (x - 4) / 2y