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Implicit Differentiation

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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Implicit Differentiation

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  1. Implicit Differentiation

  2. 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)

  3. Some Graphs of Implicitly Defined Expressions

  4. Graph of x-2xy=2

  5. Graph of x2+y2=1

  6. Graph of cos(x2)-sin(y2)=0

  7. 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.

  8. Graph of x-2xy=2 Find the equation of the tangent line at the point (2,0)

  9. Graph of x2+y2=1 Find the equation of the tangent line at the point (√0.5, √0.5)

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