Chapter 2: Q 39. (page 222)

Find the derivatives of each of functions in Exercises 17–44. In some cases it may be convenient to do some preliminary algebra.
$f (x) = \sqrt{\log_{2} (3^{x} - 5)}$

Short Answer

Expert verified

The required answer is $\frac{1}{2} {(\log_{2} (3^{x} - 5))}^{- \frac{1}{2}} (\frac{1}{\ln 2 (3^{x} - 5)} (\ln 3) 3^{x})$ .

Step by step solution

Step 1. Given information.

The given function is:

$f (x) = \sqrt{\log_{2} (3^{x} - 5)}$

Step 2. Find the derivative of the given function.

$f (x) = \sqrt{\log_{2} (3^{x} - 5)} f' (x) = \frac{d}{d x} {(\log_{2} (3^{x} - 5))}^{\frac{1}{2}} = \frac{1}{2} {(\log_{2} (3^{x} - 5))}^{- \frac{1}{2}} \frac{d}{d x} (\log_{2} (3^{x} - 5)) = \frac{1}{2} {(\log_{2} (3^{x} - 5))}^{- \frac{1}{2}} \cdot \frac{1}{\ln 2 (3^{x} - 5)} \cdot \frac{d}{d x} (3^{x} - 5) = \frac{1}{2} {(\log_{2} (3^{x} - 5))}^{- \frac{1}{2}} \cdot \frac{1}{\ln 2 (3^{x} - 5)} \cdot \ln 3 \cdot 3^{x} = \frac{1}{2} {(\log_{2} (3^{x} - 5))}^{- \frac{1}{2}} (\frac{1}{\ln 2 (3^{x} - 5)} (\ln 3) 3^{x})$

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Find the derivatives of each of functions in Exercises 17–44. In some cases it may be convenient to do some preliminary algebra.
$f (x) = \sqrt{\log_{2} (3^{x} - 5)}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the derivative of the given function.

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Find the derivatives of each of functions in Exercises 17–44. In some cases it may be convenient to do some preliminary algebra.fx=log23x-5

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the derivative of the given function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Probability and Statistics

Logic and Functions

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the derivatives of each of functions in Exercises 17–44. In some cases it may be convenient to do some preliminary algebra.
$f (x) = \sqrt{\log_{2} (3^{x} - 5)}$