View Full Version : How to find implicit differentiation?
bnhunter
Nov 12, 2010, 05:55 PM
x^2+3xy+y^2
bnhunter
Nov 12, 2010, 06:12 PM
x^2y^3 - 6xy^2 = 10
Unknown008
Nov 12, 2010, 11:05 PM
Yes, we do offer free help, but not 'free answers'... =/
Do you know how to differentiate an expression with one variable?
\frac{d}{dx}(2x^2 + 1) = 4x
So, you can express the derivative of what you got as:
\frac{d}{dx}(x^2+3xy+y^2) = \frac{d}{dx}(x^2)
\frac{d}{dx}(3xy) + \frac{d}{dx}(y^2)
You can differentiate the first part?
For the second part, let me give you an example.
\frac{d}{dx}(4y + y^2) = 4 \frac{dy}{dx} + 2y\frac{dy}{dx}
As you can see, you differentiate the y similar to how you differentiate x, but you just add dy/dx after differentiating.
For the middle part of your problem, use the product rule.
galactus
Nov 13, 2010, 10:21 AM
If I may. Allow me to show a method I often use for implicit diff.
Use \frac{-F_{x}}{F_{y}}
i.e. x^{2}y^{3}-6xy^{2}=10
-F_{x}=-2y^{2}(xy-3)
F_{y}=3xy(xy-4)
\frac{-F_{x}}{F_{y}}=y'=\frac{-2y(xy-3)}{3x(xy-4)}
Just a thought if anyone is interested.
Unknown008
Nov 14, 2010, 03:00 AM
I wasn't sure what you did at first, but when I expanded it, I understood. Interesting method :)
You only missed a 'y' in the denominator ;)