121616949-math.92 - ln a is often useful and sometimes...

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78 Chapter 4 Transcendental Functions we can take the logarithm base a of both sides to get log a ( x ) = log a ( e ln x ) = ln x log a e. Then d dx log a x = 1 x log a e. Finally, since a = e ln a log a ( a ) = log a ( e ln a ) = ln a log a e 1 = ln a log a e 1 ln a = log a e, we can replace log a e to get d dx log a x = 1 x ln a . You may if you wish memorize the formulas d dx a x = (ln a ) a x and d dx log a x = 1 x ln a . Because the “trick” a =
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Unformatted text preview: ln a is often useful, and sometimes essential, it may be better to remember the trick, not the formula. EXAMPLE 4.5 Compute the derivative of f ( x ) = 2 x . d dx 2 x = d dx ( e ln 2 ) x = d dx e x ln 2 = ± d dx x ln 2 ¶ e x ln 2 = (ln 2) e x ln 2...
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