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QUIZ 2.3, 2.4, MOTION
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LESSON #22 OBJECTIVE:
Today, I will…
…use implicit differentiation to find the derivative of a function
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EXPLICIT VS IMPLICIT FORM:
Explicit Form:
An explicit function is one which is given in terms of the independent variable.
Example:
Implicit Form:
Implicit functions, on the other hand, are usually given in terms of both dependent and
independent variables.
Example:
IMPLICIT DIFFERENTIATION
In mathematics, some equations in x and y do not explicitly define y as a function x and cannot
be easily manipulated to solve for y in terms of x, even though such a function may exist.
Implicit differentiation allows you to find the derivative of y with respect to x without having
to solve the given equation for y. The chain rule must be used whenever the function y is
being differentiated because of our assumption that y may be expressed as a function of x.
EXAMPLE
Find
given that
L22 Calculus Page 1
EXAMPLE
Determine the slope of the graph of
at the point
.
PRACTICE
Find the derivative of:
5.
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HOMEWORK
p. 146 (1-29 EOO)
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