Question

Implicit Differentiation

Answer 1

I'm trying to understand, so I put the derivative of y^4 in my calculator and it keeps giving me zero?

Answer 2

I have 10x + ___ = 0

Answer 3

5x^2 + y^4 = -9

10x + 4y^3 * dy/dx = 0

10 + 12y^2 * (dy/dx)^2 + 4y^3 * d2y/dx2 = 0

Answer 4

Find the value of dy/dx from the 1st eqn , substitute in the second.

Answer 5

This is probably a really silly question, but where did the (dy/dx)^2 come from?

Answer 6

The only part that I'm getting from the second derivative is the 10 + 12y^2. Am I meant to add the first derivative?

Answer 7

I solved and got -5x/2y^3

Answer 8

10x + 4y^3 * dy/dx = 0

when differentiating this, it's the same as the product of two functions

y * dy/dx -> derivative of y = dy/dx = (dy/dx)^2


when you derive the first derivative you get the second one

dy/dx = dy2/d2x