AP Calc BC stuff you must know cold

Critical Points

Points on a graph where the derivative is zero or undefined, indicating potential local maxima, minima, or inflection points.

dy/dx sin(x) =

cos(x)

dy/dx cos(x) =

-sin(x)

dy/dx tan(x) =

sec²(x)

dy/dx csc(x) =

-csc(x)cot(x)

dy/dx sec(x) =

sec(x)tan(x)

dy/dx cot(x) =

-csc²x

What is buddy points relationship?

If f has (a,b) and f^-1(x) has (b,a) then (f^-1)’(b) = 1/(f’(a))

dy/dx arcsin(x) =

du/((1-u²)^1/2)

dy/dx arccos(x) =

du/(-(1-u²)^1/2)

dy/dx arctan(x) =

du/(1+u²)

dy/dx arccsc(x) =

du/(-(1+u²))

dy/dx arcsec(x) =

du/|u|(u²-1)

dy/dx arcsec(x) =

du/-(|u|(u²-1))

d/dx(e^u) =

e^u(du/dx)

d/dx(a^u) =

(ln a)(a^u)(du/dx)

d/dx(ln u) =

(1/u)(du/dx)

d/dx (log_au) =

(1/ln a)(1/u)(du/dx)

Limit definition of definite integral