Calculus Methods
05 Implicit Differentiation
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The key is to remember the product rule. If you are
taking the derivative with respect to x, then any
time you take the derivative involving a variable
other
than x, you must multiply the result by the
derivative of that variable. In all of the steps and
examples, we assume that we are looking for
.
1) Take the derivative of each term on both sides of
the equation.
2)
Keep all terms involving
on one side
of the
equation, and all other terms on the other side.
3)
Solve for
.
Example:
Find
for the curve
.
1)
Note that we used the product rule to take the
derivative of
.
2)
3)
Example
#2: Find
for the curve:
.
1)
2)
3)
