Studied by 5 peopleCalculus
Derivatives & Differentiation
AP Calculus AB
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Contains vocabulary and concepts from Chapter 4 of Calculus: Concepts and Applications by Paul A. Foerster as taught by Colin Suehring at McFarland High School
the product rule
if y = uv, where u and v are differentiable functions of x, then y’= u’v + uv’
derivative of the first times second, plus first times derivative of second
the quotient rule
if y = u/v, where u and v are differentiable functions, and v doesn’t = 0, then y’ = (u’v = uv’)/v²
the quotient rule rhyme
low d high, minus high d low, square the bottom, and away we go!
sin’x
cosx
cos’x
-sinx
tan’x
sec²x
cot’x
-csc²x
sec’x
secx tanx
csc’x
-cscx cotx
tanx
sinx/cosx
cotx
cosx/sinx
secx
1/cosx
cscx
1/sinx
sin²x + cos²x =
1
1 + cot²x =
csc²x
tan²x + 1 =
sec²x
derivative of the inverse function
if y = f⁻¹(x), then d/dx (f-1(x)) =
1/ (f’(f⁻¹(x))
d/dx (sin-1x)
1/√1-x²
d/dx (cos-1x)
-1/√1-x²
d/dx (tan-1x)
1/1+x²
d/dx (cot-1x)
-1/1+x²
d/dx (sec-1x)
1/|x|√x²-1
d/dx (csc-1x)
-1/|x|√x²-1
if a function f is differentiable at a point x=c, then
f is continuous at x=c
if a function f is not continuous
it is not differentiable
related rates
D.R.E.D.S.
Note
Flashcard