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Chapter 2: Q.35 (page 198)

Use the differentiation rules developed in this section to find

the derivatives of the functions

f(x)=4-x7

Short Answer

Expert verified

The derivative off(x)=4-x7is-7x6

Step by step solution

01

Step1. Given information

Here function f(x)=4-x7is given.

we have to find out the derivatives of this function

02

Step2. finding the derivatives of the function

By using the power rule, we can solve this problem.

Power rule: For any nonzero rational number k,

ddxxk=kxk-1

Thus using this power rule when we do the differentiation , we get

ddx(4-x7)=d(4)dx-d(x7)dx=0-7x6sincederivativeofaconstantis0=-7x6thusthederivativeofgivenfunctionis-7x6

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Most popular questions from this chapter

For each function graphed in Exercises 65-68, determine the values of xat which ffails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.

For each function f and value x=cin Exercises 35–44, use a sequence of approximations to estimate f'(c). Illustrate your work with an appropriate sequence of graphs of secant lines.

f(x)=4-x2,c=1

The total yearly expenditures by public colleges and universities from 1990 to 2000 can be modeled by the function E(t)=123(1.025)t, where expenditures are measured in billions of dollars and time is measured in years since 1990.

(a) Estimate the total yearly expenditures by these colleges and universities in 1995.

(b) Compute the average rate of change in yearly expenditures between 1990 and 2000.

(c) Compute the average rate of change in yearly expenditures between 1995 and 1996.

(d) Estimate the rate at which yearly expenditures of public colleges and universities were increasing in 1995.

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)=3x5-2x2+4;f(0)=1

Use the definition of the derivative to find f'for each function fin Exercises 39-54

role="math" localid="1648290170541" f(x)=x-1x+3
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