1. FIRST DERIVATIVES OF IMPLICIT FUNCTIONS
Learning Outcomes:
Know the difference between implicit and explicit functions
Be able to differentiate functions in implicit form

2. We can already differentiate explicit functions
Implicit Form
Explicit Form
two explicit functions →implicit function is a multi-valued function
We can already differentiate explicit functions

3. Find in terms of x and y for the implicit function
Ex4A
no.1a
Find in terms of x and y for the implicit function
Differentiate each term with respect to x.
Since y is a function of x, the product rule must be used to get the derivative of xy
Since y is a function of x, the chain rule must be used to get the derivative of y2
outer function
inner function
Page 36
Ex 4A
nos 1

4. Differentiate each term with respect to x.
Example
Find the gradient of the tangent at A(3, -4) to the circle with equation
Differentiate each term with respect to x.
Since y is a function of x, the chain rule must be used to get the derivative of y2
outer function
inner function
the gradient of the tangent at A(3, -4) =

5. http://www. math. ucdavis
Great worked examples on this page