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Derivatives and Integrals Rules and Techniques, Quizzes of Differential Equations

Virginia Polytechnic Institute and State University (Virginia Tech)Differential Equations

Definitions and rules for calculating derivatives and integrals, including the sum, product, quotient, chain, and power rules. It also covers the concept of a constant and the integration of basic functions such as exponential, trigonometric, and logarithmic functions.

Typology: Quizzes

2010/2011

Uploaded on 05/25/2011

lusher
lusher 🇺🇸

5 documents

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TERM 1
[ f(x) +- g(x) ]'
DEFINITION 1
= f '(x) +- g ' (x)
TERM 2
[ c f(x) ]'
DEFINITION 2
c f '(x)
TERM 3
[ f(x) g(x) ] Product Rule
DEFINITION 3
f '(x)g(x) + f(x)g'(x)
TERM 4
[ f(x) / g(x) ]' Quotient
Rule
DEFINITION 4
f '(x)g(x) - f(x)g'(x) g^2(x)
TERM 5
[ f(g(x)) ]' Chain Rule
DEFINITION 5
f '(g(x))g'(x)
pf3

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[ f(x) +- g(x) ]'

= f '(x) +- g ' (x)

TERM 2

[ c f(x) ]'

DEFINITION 2

c f '(x)

TERM 3

[ f(x) g(x) ] Product Rule

DEFINITION 3

f '(x)g(x) + f(x)g'(x)

TERM 4

[ f(x) / g(x) ]' Quotient

Rule

DEFINITION 4

f '(x)g(x) - f(x)g'(x) g^2(x)

TERM 5

[ f(g(x)) ]' Chain Rule

DEFINITION 5

f '(g(x))g'(x)

If f '(x) = 0 everywhere

f(x) = constant

TERM 7

(sinx)' (cosx)' (e^x)' (lnx)' (x^n)'

DEFINITION 7

cosx-sinxe^x1/x(n)(x^n-1)

TERM 8

int( f(x)+g(x) )dx

DEFINITION 8

int(f(x))dx +- int(g(x))dx

TERM 9

int( C f(x)) dx

DEFINITION 9

C* int(f(x))dx from a to b

TERM 10

int(f(x))dx from a to b

DEFINITION 10

= int(f(x))dx from a to c +- int(f(x))dx from c to b