Unit 1 Properties Flashcards
1/sinx =
cscx
1/cosx
secx
1/tanx
cotx
pythag for sin
sin^2x+cos^2x=1
pythag for tan
1+tan^2x=sec^2x
pythag for cot
1+cot^2x=csc^2x
pythag for cos
sin^2x+cos^2x=1
pythag for sec
1+tan^2x=sec^2x
pythag for csc
1+cot^2x=csc^2x
d/dx(lnx) =
1/x for x>0
d/dx(log sub b of x) =
1/xlnb for x>0
d/dx(b^x) =
b^x * lnb
d/dx(secx) =
secx * tanx
d/dx(cscx) =
MINUS cscx * cotx
d/dx(tanx) =
sec^2x
d/dx(cotx) =
MINUS csc^2x
d/dx(sin^-1x) =
1 / root(1-x^2)
* or negative cos^-1
d/dx(cos^-1x) =
MINUS 1 / root(1-x^2)
* or negative sin^-1
d/dx(tan^-1x) =
1 / (1+x^2)
* or sin^-1/cos^-1 without root
d/dx(cot^-1x) =
MINUS 1 / (1+x^2)
* or negative tan^-1
derivative product rule
left d,right + right d,left
derivative quotient rule
low d,high - high d,low / low^2
d/dx(f(g(x))) chain rule
fprime(g(x)) * gprime(x)
∫(1/x)dx =
ln|x| + C
∫sec^2xdx =
tanx + C
∫csc^2xdx
MINUS cotx + C
∫secx * tanx dx =
secx + C
∫cscx * cotx dx =
MINUS cscx + C
∫b^x dx =
(1/lnb) * b^x + C
∫log sub b of x dx
(1/lnb) * ∫lnxdx
∫tanxdx =
MINUS ln|cosx| + C
∫cotxdx =
ln|sinx| + C
∫secxdx =
ln|secx + tanx| + C
∫cscxdx =
ln|cscx - cotx| + C
washer method
V = pi * a to b∫ (bigr^2 - smallr^2)dx
1/cscx =
sinx
1/secx =
cosx
1/cotx =
tanx
