Chain Rule, Implicit Differentiation, Inverse & Log functions

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Lec 16 - the chain rule, implicit differentiation. If g is differentiable at x and f is differentiable at ) then is differentiable at and (proof p 199; sketch 204-205) Sometimes we have to be more clever in calculating a derivative if the function is not in the form we expect . But it can be broken into 2 functions. and. We can calculate the derivative in each case: So the slope at is and at is . Sometimes difficult to solve relations for y, ex. We can instead be sneaky and differentiate directly, with respect to x, remembering that is a function of . When does the derivate not exist? tells us when tells us when . Lec 17 - derivatives of inverse functions, logarithmic. Find the tangent to the curve at . Do not solve for , plug in the point .

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