and the independent variable 
but where neither variable is the subject of the equation. [M4.3]
is: a form of differentiation using the chain rule. [M4.3]
is used: for differentiating implicit functions which are defined by an equation that relates the dependent variable and the independent variable but where neither variable is the subject of the equation. [M4.3]
is done: by differentiating both sides of the equation, which yields, in general, an expression in 
and 
for 
[M4.3]
is exemplified: by implicit differentiation of 
with respect to 
which yields 
so that 
[M4.3]
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