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Chapter 2: Q 31. (page 222)

Find the derivatives of each of functions in Exercises 17鈥�44. In some cases it may be convenient to do some preliminary algebra.

fx=lnx5lnx4

Short Answer

Expert verified

The required answer isf'x=0.

Step by step solution

01

Step 1. Given information.

The given function is:

fx=lnx5lnx4

02

Step 2. Find the derivative of the given function.

fx=lnx5lnx4

We know that logam=mloga, therefore,

fx=5lnx4lnx=54

We know that the derivative of a constant term is 0, and in the given question all the terms are constant therefore the derivative is 0.

f'x=0

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Most popular questions from this chapter

A tomato plant given xounces of fertilizer will successfully bear T(x)pounds of tomatoes in a growing season.

(a) In real-world terms, what does T(5)represent and what are its units? What does T'(5)represent and what are its units?

(b) A study has shown that this fertilizer encourages tomato production when less than 20ounces are used, but inhibits production when more than 20ounces are used. When is T(x)positive and when is T(x)negative? When is T'(x)positive and when is T'(x)negative?

If Katie walked at 3miles per hour for 20minutes and then sprinted at 10miles an hour for 8minutes, how fast would Dave have to walk or run to go the same distance as Katie did at the same time while moving at a constant speed? Sketch a graph of Katie鈥檚 position over time and a graph of Dave鈥檚 position over time on the same set of axes.

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The tangent line to f(x)=x2 atx=-3

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=1x-3x2x5-1x

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=x(4-2x);f(0)=0
See all solutions

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