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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.
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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)
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)