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Chapter 2: Q. 0 (page 197)

Problem Zero: Read the section and make your own summary of the material.

Short Answer

Expert verified

Rules for calculating basic derivatives

Step by step solution

01

Step 1. Given Information

Realnumber:k,m,b.Functions:f(x),g(x)

02

Step 2. Summary

Forrealnumberk,m,b:ddx(mx+b)=mddx(xk)=k.xk-1Constantmultiplerule:ddx(k.f(x))=k.f'(x)Sumrule:ddx(f(x)+g(x))=f'(x)+g'(x)Differencerule:ddx(f(x)-g(x))=f'(x)-g'(x)Productrule:ddx(f(x).g(x))=f(x).g'(x)+f'(x).g(x)Quotientrule:ddxf(x)g(x)=g(x).f'(x)-f(x).g'(x)g(x)2

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Most popular questions from this chapter

Prove that if f is a quadratic polynomial function f(x)=ax2+bx+cthen the coefficient of f are completely determined by the values of f(x) and its derivatives at x=0 as follows

a=f"(0)2;b=f'(0);c=f(0)

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

f(x)=x(3x2+1)9

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)=7x2+8x11-18;f(0)=-2

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

f(x)=x2-x3+5x9x-1

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

f(x)=x2+1
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