   Chapter 2.R, Problem 59E

Chapter
Section
Textbook Problem

# Suppose that   f ( 1 ) = 2     f ' ( 1 ) = 3      f ( 2 ) = 1      f ' ( 2 ) = 2 g ( 1 ) = 3     g' ( 1 ) = 1     g ( 2 ) = 1    g' ( 2 ) = 4 (a) If S ( x ) = f ( x ) + g ( x ) , find S ' ( 1 ) (b) If P ( x ) = f ( x ) g ( x ) , find P ' ( 2 ) (c) If Q ( x ) = f ( x ) / g ( x ) , find Q ' ( 1 ) (d) If C ( x ) = f ( g ( x ) ) , find C ' ( 2 )

To determine

(a)

To find:

S'1

Explanation

1) Formula:

i. Sum rule:

ddxfx+gx=ddxfx+ddxg(x)

ii. Difference rule:

ddxfx-gx=ddxfx-ddxg(x)

iii. Product rule:

ddx[fx.g(x)]=f(x)ddxgx+g(x)ddxf(x)

iv

To determine

(b)

To find:

P'(2)

To determine

(c)

To find:

Q'(1)

To determine

(d)

To find:

C'(2)

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