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Chapter 2: Q. 37 (page 210)

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)=53x4-13+3x-1100

Short Answer

Expert verified

The required answer is10053x4-13+3x-199180x33x4-12+3

Step by step solution

01

Step 1. Given Information  

The given function is f(x)=53x4-13+3x-1100

02

Step 2. Calculation   

Differentiate both the sides with respect tox, we get,

f'(x)=ddx53x4-13+3x-1100=10053x4-13+3x-1100-1ddx53x4-13+ddx(3x)-ddx1=10053x4-13+3x-1995(33x4-13-1)ddx(3x4-1)+3=10053x4-13+3x-199153x4-12)(12x3)+3=10053x4-13+3x-199180x33x4-12+3

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Most popular questions from this chapter

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

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

The line that passes through the point (3,2)and is parallel to the tangent line to f(x)=1x at x=-1.

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=0

The following reciprocal rules tells us hoe to differentiate the reciprocal of a function

ddx(1f(x))=-1[f(x)]2

Prove this using

a) definition of the derivative

b) by using the quotient rule

For each function fgraphed 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.
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