MATH127 Lecture Notes - Lecture 3: Glossary Of Video Game Terms, Dependent And Independent Variables, Pythagorean Theorem

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You should read section 3. 6 of the textbook and do exercises 5, 7, 13, 15, 19. We can use implicit di erentiation to nd the derivative of logarithmic functions. Suppose y = loga x. rewrite this as an exponential ay = x and di erentiate both sides implicitly with respect to x. d dx ay ln a dy dx dy dx ay = d dx x. 1 x ln a d dx loga x = Note that when a = e, we have d dx ln x = In fact, we have d dx ln|x| = Calculating derivatives of complicated functions (involving combination of products, quotients, and exponents) can often be simpli ed by rst taking the natural logarithm of both sides, using some alge- braic properties of logs, and then di erentiating both sides implicitly. Find the derivative of y = x3/4px2 + 1 (3x + 2)5.

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