Implicit differentiation is the procedure of differentiating an implicit equation with respect to the desired variable 
while treating the other variables as unspecified functions
of 
.
For example, the implicit equation
 |
(1)
|
can be solved for
 |
(2)
|
and differentiated directly to yield
 |
(3)
|
Differentiating implicitly instead gives
![d/(dx)[xy]=d/(dx)[1]](/images/equations/ImplicitDifferentiation/Inline3.svg) |
(4)
|
 |
(5)
|
 |
(6)
|
 |
(7)
|
Plugging in 
verifies that this approach gives the same result as before.
Implicit differentiation is especially useful when 
is needed, but it is difficult or inconvenient to solve
for 
in terms of 
.
