Implicit derivative at a point (no calculator)

Question

Given the equation of the curve 2x²-3xy+y = 10, find dy/dx at the point (0, 10).

A. -30

B. 0

C. 30

D. 40

Answer 1

Implicitly differentiate the function. Remember to use the chain rule:

2x² - 3xy + y = 10 : u = -3x v = y

(d/dx):

4x - 3y - 3xy' + y' = 0

isolate y'

-3xy' + y' = -4x + 3y

y' (1-3x) = 3y-4x

y' = (3y - 4x)/(1 - 3x)

evaluate at (0,10)

dy/dx = (3(10) - 4(0))/(1-3(0))

dy/dx = 30

Answer 2