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Implicit Differentiation
Implicitly vs. Explicitly Defined Functions
y is given explicitly as a function of x (y is solved in terms of x)
y is given implicitly as a function of x (y is NOT solved in terms of x)
Some Graphs of Implicitly Defined Expressions
Graph of x-2xy=2
Graph of x2+y2=1
Graph of cos(x2)-sin(y2)=0
Implicit Differentiation
When y is not given explicitly as a function of x, think of y as “locally” being a function of x.
This approach is used to differentiate expressions where a term in the expression is considered implicitly as a function of another variable.
Graph of x-2xy=2
Find the equation of the tangent line at the point (2,0)
Graph of x2+y2=1
Find the equation of the tangent line at the point (√0.5, √0.5)
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