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Implicit Differentiation

Implicit Differentiation. 2.5a. Implicit Differentiation. So far, all the equations and functions we looked at were all stated explicitly in terms of one variable:.

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Implicit Differentiation

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  1. Implicit Differentiation 2.5a

  2. Implicit Differentiation So far, all the equations and functions we looked at were all stated explicitly in terms of one variable: In this function, y is defined explicitly in terms of x. If we re-wrote it as xy = 1, y is now defined implicitly in terms of x. It is easy to find the derivative of an explicit function, but what about:

  3. This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

  4. 1 Differentiate both sides w.r.t. x. 2 Solve for . This can’t be solved for y. This technique is called implicit differentiation.

  5. Find dy/dx if:

  6. Homework2.5a (pg. 146); #1-4, 21, 22

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