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IMPLICIT DIFFERENTIATION Tutorial

IMPLICIT DIFFERENTIATION Tutorial. Math 135 Rutgers University TA: Diego Penta Recitation SEC 16-18 Questions: Send mail to penta@math.rutgers.edu. Use arrow keys or click mouse to advance from step to step. dy dx. Find , given:. 3. 3. ( x y ). ( x y ). e. e. exp ( x y ). 3.

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IMPLICIT DIFFERENTIATION Tutorial

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  1. IMPLICIT DIFFERENTIATION Tutorial Math 135 Rutgers University TA: Diego Penta Recitation SEC 16-18 Questions: Send mail to penta@math.rutgers.edu Use arrow keys or click mouse to advance from step to step

  2. dy dx Find , given: 3 3 (xy) (xy) e e exp(xy) 3 PROBLEM – x x 2 2 Term 1 Term 1 = xy xy 3 3 Term 3 To make the exponential easier to read, I will write Term 1 as exp(x y). Term 2 3 I will color-code the terms, for clarity. I will refer to some page numbers in the book. Spend time understanding each step before continuing.

  3. d dx dy dx Term 3: Remember, (yn) = nyn-1 dy dx SOLUTION d dx   (x3y) dy dx dy dx dy dx dy dx Don’t forget the here! 4) We now have an equation relating x, y, and … ! – 2x 5) Using algebra, we now isolate on one side of the equation to obtain our answer: Distributing exp(x3y) will make things a whole lot easier! 1) Differentiate both sides with respect to x (page 147). Use the extended linearity rule (p.114). 2) Use chain rule (p.140). Use power rule (p.111). Use product rule (p.113). – 2x 3) Term 1: Now use product rule. Remember parentheses! = – 2x ANSWER:

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