definition of e
definition of absolute value
definition of the derivative
alternative definition of the derivative
definition of continuity
average rate of change of f(x) on [a,b]
intermediate value theorem
if f is continuous on [a,b] and k is any number between f(a) and f(b), then there is at least one number c between a and b such that f(c) = k
what does d/dx [c] equal?
= 0
derivative product rule
d/dx [f(x)g(x)] = f’(x)g(x) + f(x)g’(x)
chain rule
d/dx (f(g(x))) = f’(g(x)) * g’(x)
power rule
quotient rule
d/dx [sin u]
= cos u du/dx
d/dx [cos u]
= - sin u du/dx
d/dx [tan u]
= sec^2(u) du/dx
d/dx [sec u]
= sec u tan u du/dx
d/dx [csc u]
= -csc u cot u du/dx
d/dx [cot u]
= - csc^2 (u) du/dx
Rolle’s Theorem
Mean Value Theorem (MVT)
definition of a critical number
definition of increasing functions
definition of decreasing functions
Test for Increasing and Decreasing functions
First Derivative Test
Second Derivative Test
definition of definite integral
integral of …
∫cos u du
sin u + c
∫sin u du
-cos u + c
∫sec²u du
tan u + c
∫sec u tan u du
sec u + c
∫csc²u du
-cot u + c
∫csc u cot u du
-csc u + c
first fundamental theorem of calculus
second fundamental theorem of calculus
integral chain rule
average value of f(x) on [a,b]
derivative of inverse function d/dx [(f^-1)(u)]
d/dx [ln u]
ln |u| + C
∫tan u du/dx
-ln |cos u| + C
∫sec u du/dx
ln |sec u tan u| + C
∫cot u du/dx
ln |sin u| + C
∫csc u du/dx
-ln |csc u + cot u| + C