IMPLICIT DIFFERENTIATION
BASIC CAL
IMPLICIT DIFFERENTIATION
Consider the derivative of
this function:
y = 2x³ + x2 + 3
IMPLICIT DIFFERENTIATION
Consider the derivative of
this function:
x2 + xy + y2 = 0
IMPLICIT DIFFERENTIATION
The majority of differentiation problems in basic calculus involves functions “y”
written explicitly as functions of the independent variable “x”. This means that
we can write the function in the form y = f(x). For such a function, we can find
the derivative directly.
However, some functions “y’ are written implicitly as functions of “x”. This
means that the expression is not given directly in the form y = f(x). But still we
can find the derivative even without writing explicitly the functional relationship.
This is accomplished via a technique usually referred to as implicit
differentiation.
Implicit Differentiation let’s us derive functions
without having to equate it to “y”.
IMPLICIT DIFFERENTIATION
Consider the derivative of
this function:
y2 - 3x2 = 6 + 5xy