What is implicit differentiation?

Example: Differentiate X^2 y + 2 y + 5x

Answer:

step 1: Differentiate each function while treating y as a constant.

This gives: 2xy + 5.

step 2: Differentiate each function while treating x as a constant. Note each time you differentiate a y, you need to times by dy/dx.

This gives: x^2 dy/dx + 2 dy/dx

Step 3: Add answers to step 1 and step 2 together which gives the final answer

Final answer: 2xy + 5 + x^2 dy/dx + 2 dy/dx