Question

Can someone explain implicit differentiation to me using my example problem?

Answer 1

\[x ^{3}-xy+y ^{2}=7\]

Answer 2

If y = f(x), then y' = f'(x). Not much more to it that that, really. Learn your Chain Rule THOROUGHLY, first!

Answer 3

x^3-xy+y^2=7
take derivative of both sides in respect of x
x^3 differentiate with respect to x which gives us 3x^2
-xy thats differentiated using product rule. first factor * the derivative of the second factor)
x*y'+y*x')
Derivative of y (chain rule)
2yy'
differentiation of 7 is 0
3x^2-xy'-yx'+2yy'=0
3x^2-yx'=xy'-2yy'
3x^2-yx'=y'(x-2y)
3x^2-yx'/x-2y=y'

Answer 4

Wow. That actually makes a lot of sense. Much more simple than I thought it would be too. Thanks!

Answer 5

good to hear that, your most welcome :D