Can someone explain Implicit Differentiation and Related Rates in Calculus?

[Azrioch]

Hi. I'm taking a Calculus course right now and I simply cannot understand Implicit Differentiation or the Related Rate problems. My textbook does not do a good job explaining it. It is a very accelerated class and I cannot get it and I need to know it in two days for a mid term.

I just don't understand the concept.. or well any of it.

Could someone explain it to me?

Thank you in advance.

 

[Hurkyl]

Forget you're doing something "fancy" and just apply the rules of differentiation... remembering that if you're differentiating with respect to, say, x, the other variables are functions of x.

e.g.

xy = 1

rememebr that y is a function of x, so write as:

x y(x) = 1

then differentiate both sides using the product rule

y(x) + x y'(x) = 1

and now if you want something interesting like y'(1), you just have an ordinary algebra problem... you have two unknowns, y(1) and y'(1), and two equations.

 

[Dx]

Hi!

here is a good site for example to help you. http://archives.math.utk.edu/visual.calculus/3/implicit.7/ I find it easier to use the power rule for finding Dx after you have all variables to one side = 0.
Dx