Calculus

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Derivative of a constant
d/dx(c)=

zero
The power rule
d/dx(xⁿ)=

nx^n-1
d/dx[cf(x)]=

c d/dx f(x)
The sum rule: d/dx[f(x) + g(x)]=

d/dx f(x) + d/dx g(x)
The difference rule:
d/dx[f(x)-g(x)]=

d/dx f(x) - d/dx g(x)
Product Rule:
(f(x)g(x))'=

fg ' + gf '. Or d/dx[f(x)g(x)]= f(x) d/dx g(x) + g(x) d/dx f(x)
Quotient Rule:
(f/g)'=

(gf ' - fg ')/g²
d/dx (sin x)=

cos x
d/dx (cos x)

- sin x
d/dx (tan x)

sec²x
d/dx (csc x)=

-csc x cot x
d/dx (sec x)=

sec x tan x
d/dx (cot x)=

-csc²x
Chain rule:
If F(x)= f(g(x)), then F(x)' =

F(x)'= f ' (g(x))g'(x). Derivative of the outer function * inner function * derivative of the inner function
Power Rule Combined with the Chain rule:
d/dx (uⁿ)=

nu^n-1 du/dx

Author

41646

Card Set

Calculus

Description

Review for rules of differentiation and integration, Stewart Textbook 5th ed.

Updated

2010-10-18T20:30:33Z

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