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Differentiation Rules: Constant, Power, Sum, Product, Quotient Rules & Examples, Exercises of Mathematics

Mathematics

An overview of various differentiation rules including the constant rule, power rule, sum rule, product rule, and quotient rule. It includes examples of how to apply these rules to different functions. Students of calculus and related fields will find this document useful for understanding the concepts of differentiation and its applications.

Typology: Exercises

2020/2021

Uploaded on 03/24/2021

hygeia-hatoza
hygeia-hatoza 🇵🇭

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Basic Differentiation Rules
The Constant Rule
The Power Rule
The Constant Multiple Rule
The Sum Rule
The Product Rule
Dx [f(x)g(x)] = f(x)g’(x) +
g(x)f’(x)
y = (3x – 1) (2x + 5)
f(x) = 3x – 1
f’(x) = 3
g(x) = 2x + 5
g’(x) = 2
y’ = (3x-1) (2) + (2x+5) (3)
= 6x – 2 + 6x + 15
= 12x + 13
pf3
pf4

Partial preview of the text

Download Differentiation Rules: Constant, Power, Sum, Product, Quotient Rules & Examples and more Exercises Mathematics in PDF only on Docsity!

Basic Differentiation Rules

The Constant Rule

The Power Rule

The Constant Multiple Rule

The Sum Rule

The Product Rule

D

x

[f(x)g(x)] = f(x)g’(x) +

g(x)f’(x)

y = (3x – 1) (2x + 5)

f(x) = 3x – 1

f’(x) = 3

g(x) = 2x + 5

g’(x) = 2

y’ = (3x-1) (2) + (2x+5) (3)

= 6x – 2 + 6x + 15

= 12x + 13

d = (2x

+ 2) (x

= (2x

+ 2) (2x) + (x

(4x)

= 4 x

+ 4x + 4 x

+ 12 x

= 8 x

+ 16x

k(u) = (4u + 5) (7u

– 5u)

k’(u) = (4u + 5) (21 u

(7u

– 5u) (4)

= 84u

+ 105 u

– 20u –

25 + 28u

– 20u

=112 u

+ 105 u

– 40u – 25

12 x

3

  • 31 x

2

  • 20 x −

12 x

3

  • 38 x

2

  • 20 x

( 3 x ¿¿ 2 + 4 x )

2

12 x

3

  • 31 x

2

  • 20 x − 12 x

3

− 38 x

2

− 20 x

( 3 x ¿¿ 2 + 4 x )

2

− 7 x

2

( 3 x ¿¿ 2 + 4 x )

2

(c)h(t) =

t

2

3

assignment deadline

5pm

send it to my gmail

[email protected]

(d) y =

x

2

x

2