Find dy/dx by implicit differentiation.

Question

Find dy/dx by implicit differentiation.

(8x + 3y)^1/3 = x²

Answer 1

(1/3)( 8x + 3y)^(-2/3) (8 + 3y') = 2x

8+3y' = 6x(8x + 3y)^(2/3)

3y' = 6x(8x + 3y)^(2/3) - 8

y' = (1/3)[6x(8x + 3y)^(2/3) - 8]

= [2x(8x+3y)^(2/3) - 8/3]