Calculus Section 2.5A
LT: Use Implicit Differentiation to Find a Derivative
Notes
โข Used if you canโt isolate y
โข Remember that you are differentiating with respect to
something
o Example: dy/dx is the derivative of y with respect to x
โข Use chain rule to deal with variables other than what you are
differentiating with respect to
o Why donโt you have to do this for x?
โข Implicit differentiationโฆ
o Differentiate both sides of equation with respect to x
o Collect all ๐๐ฆ
๐๐ฅ terms on one side of the =
o Factor and isolate ๐๐ฆ
๐๐ฅ
Examples
Find the derivative.
1)
๐
๐๐ฅ [๐ฆ2]= 0
2)
๐ฅ2+๐ฆ2=25
3)
๐ฅ2๐ฆ+๐ฅ๐ฆ2= 6
