   Chapter 2.7, Problem 33E

Chapter
Section
Textbook Problem

Find f'(a). f ( t ) = 2 t + 1 t + 3

To determine

To find: The derivative of the function f(t)=2t+1t+3 at t=a.

Explanation

Formula used:

The derivative of a function at a number a, denoted by f(a) is,

f(a)=limh0f(a+h)f(a)h (1)

Calculation:

Obtain the derivative of the function f(t) at t=a.

Use the equation (1) to compute f(a).

f(a)=limh0f(a+h)f(a)h=limh0(2(a+h)+1(a+h)+3)(2a+1a+3)h=limh0(2(a+h)+1)(a+3)(2a+1)((a+h)+3)((a+h)+3)(a+3)h=limh0(2a+2h+1)(a+3)(2a+1)(a+h+3)h(a+h+3)(a+3)

Expand the numerator and simplifying further as follows,

f(h)=limh0a(2a+2h+1)+3(2a+2h+1)2a(

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