Calculus 1 - implicit differentiation
posted by Cupcake on .
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.
if you can do the basic rules like the product rule, then you can do implicit differentiating.
Let me explain term by term
xy is a product, so when you differentiate
x(dy/dx) + y(dx/dx)
x(dy/dx) + y since dx/dx = 1
2x would give you 2 and
3x^2 would give you 6x (really it was 6x(dx/dx) which is 6x(1) or 6x)
and of course the derivative of 4 is zero
so you would have
x(dy/dx) + y + 2 + 6x = 0
solving this for dy/dx you would finally have
dy/dx = (-6x - y - 2)/x
You will get questions where there is a dy/dx in several terms.
In that case bring all those terms to one side of your equation, factor out the dy/dx, and solve for dy/dx that way.
the key this is to remember:
if you differentiate an x term you also get a dx/dx hanging around, which is 1, so you don't have to write it, but
if you differentiate a y term you would get a dy/dx hanging around.