Term Test 2
Prof: Olga Brezhneva
Chapter 3 Differentiation Rules
3.5 Implicit Differentiation
Implicit Function: An implicit function is a function that is defined implicitly by an implicit equation, by
associating one of the variables (the value) with the others (the arguments).
2. Implicit Differentiation
For implicit function, we don’t need to solve for y in term of x in order to find y’. What we can do it
differentiate both side of the function with respect to x, then solving the resulting question for y’.
Suppose that , ( y implicitly as a function of x ). If we want to find
, we need to
differentiate the entire equation with respect to x. Remember that y is also a function of x.
The above process to find
is called implicit differentiation.
Past Exam Questions:
1. Given , express
in terms of x and y. Evaluate at ( 0, 1 ).
Differentiate both side with respect to x:
At the point (0,1),
2. Given , find
Then we have:
On the left side:
On the right side: