Question

I do not understand implicit differentiation. One of the problems are: find y' by implicit differentiation xy+2x+3x^2=4.

I would appreciate any help that can be offered.

Answer 1

Just differtiate each term with respect to x, remembering that y is a function of x. You often end up with an expression for y' that involves both x and y, but is is a valid equation. You may have to evaluate y before you can calculate y'. Here is what you get:

x*dy/dx + y + 2 + 6x = 0
dy/dx = -(y + 2 + 6x)/x
= -(y+2)/x -6

Answer 2

thank you