Diberikan persamaan x2+y3= x+1. Tentukan turunan dy/dx dan d2y/dx2

jawab

x² + y³ = x+ 1
y³ = - x²  + x + 1

y = (- x² + x + 1)^(1/3)

dy/dx =  1/3 (- x² + x + 1)^(-2/3 . (-2x + 1)
dy/dx = 1/3 (-2x +1) (-x² + x + 1)^(-2/3)
dy/dx = (-2/3 x + 1/3)(-x² + x + 1)^(-2/3)

d2y/dx2 = (-2/3)(-x² + x +1)^(-2/3) + (-2/3 x + 1/3)(-2/3)(-x^2+x +1)^(-5/3) (-2x +1)