Derivatives | MATH - Calculus 1 - Introduction, Quizzes of Calculus

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sin (u)

cos (u)

TERM 2

cos (u)

DEFINITION 2

-sin (u)

TERM 3

tan (u)

DEFINITION 3

sec^2 (u)

TERM 4

cot (u)

DEFINITION 4

-csc^2 (u)

TERM 5

sec (u)

DEFINITION 5

sec (u) tan (u)

csc (u)

-csc (u) cot (u)

TERM 7

chain rule (u-substitution)

DEFINITION 7

Old Formula: d/dx (x^n)=nx^n-1 New Formula: u = function

d/dx u^n = nu ^(n-1) du/dx

TERM 8

The derivative of f(x)

DEFINITION 8

f'(x)= lim f(x+h) - f(x)/h h->

TERM 9

Physical interpretations of f(x)

DEFINITION 9

1) slope of the tangent line 2) instantaneous speed

TERM 10

step 1 find the equation of the tangent line

DEFINITION 10

f(x)=3x^2-x+4 1) Find f'(x) f(x+h)=3(x+h)^2-(x+h)+

3x^2+6xh+3h^2-x-h+4 -f(x) 3x^2 -x +4 6xh+3h^2 -h

6xh+3h^2-h/h= 6x+3h-1 f'(x) 6x+3h-1=6x+3(0)-1= 6x-

lim h->