Page 181 - Calculus Demystified

168 SOLUTION CHAPTER 6 Transcendental Functions
We have
d x −π =−π · x −π−1 ,
dx
d √ 3 √ √ 3−1
dx x = 3 · x ,
d e e−1
dx x = e · x .
sin x−x 2 4π
You Try It: Calculate (d/dx)5 . Calculate (d/dx)x .
6.4.2 GRAPHING OF LOGARITHMIC AND

EXPONENTIAL FUNCTIONS
If a> 0 and f(x) = log x, x > 0, then
a
1

f (x) = x · ln a
−1

f (x) = x · ln a
2
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f(1) = 0.

Using this information, we can sketch the graph of f(x) = log x.
a

If a> 1 then ln a> 0 so that f (x) > 0 and f (x) < 0. The graph of f is
exhibited in Fig. 6.6.

Fig. 6.6
If 0 <a < 1 then ln a =− ln(1/a) < 0 so that f (x) < 0 and f (x) > 0. The

graph of f is sketched in Fig. 6.7.
Since g(x) = a is the inverse function to f(x) = log x, the graph of g is the
x
a
reflection in the line y = x of the graph of f (Figs 6.6 and 6.7). See Figs 6.8, 6.9.

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