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MATH 201 Section 3 Summary of Two Differentiation Rules Mathematics Worksheet

MATH 201

MATH

### Question Description

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Two pages summary about Section 3.2 The product/Quotient Rule, and Section 3.3 The Chain Rule.

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Summary of two differentiation rules
This report summarizes two differentiation rules from sections 3.2 and 3.3 of the textbook.
The two rules are
1) The product/quotient rule
2) The chain rule

The product rule
The product rule states that the derivative of the product of two differentiable functions is given
by
u '( x) = f ( x) g '( x) + f '( x) g ( x)

where
f ( x ) = the first function, whose derivative is f ' ( x ) ,
g ( x ) = the second function, whose derivative is g ' ( x ) ,
u ( x ) = f ( x ) g ( x ) , the product of the two functions.
Example
Problem:
Find the derivative of the function ( 3x3 − 2 x 2 + 5 x − 1) x + x

(

)

Solution:
Let f ( x ) = 3x3 − 2 x 2 + 5 x − 1, g ( x ) = x + x , so that u ( x ) = f ( x ) g ( x ) .
f ' ( x ) = 9x2 − 4x + 5
g '( x) = 1+

1 −1/2
1
x = 1+
2
2 x

Therefore

(

1 

2
u '... abotsi55 (1152)
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