Find f-1(x)
Inverse of f(x) switch x & y and solve for y~
Derivatives
df-1/fc=1/(df/dx)
d/dx ln(x) = 1/x
d/dx ln(u) = 1/u du/dx
d/dx ln(x^2+3) = 1/(x^2+3)* dy/dx(x^2+3) = 1/(x^2+3)*2x = 2x/(x^2+3)
the deriv of y=ln(ax) = 1/x for all a~
Log Diffs of y=f(x)
1. take log of both sides and simplify
2. Differentiate implicitly
3. Solve for dy/dx
4. Subst for y~
Math rules for logs
1. ln(ax) = ln a _ ln x
2. ln(a/x) = ln a - ln x
3. ln(1/x) = -ln x
4. ln(x^n) = n ln x~
Log roots
ln nth root of x = 1/n ln(x)~
Integrals
int(1/u)du = ln|u| +C
int(tan(u))du = ln(|cos u| +C = ln|sec u| +C
int(cot(u))du = ln|sin u| +C = -ln|csc u| +C~
Half Life
HalfLife = ln(2)/k~
Law Expon Change
y=y0*e^(kt)
k is rate constant of equation~
Triangles
arccot(x) = Pi/2 -arctan(x)
arcsec(x) = arccos(1/x)
arccsc(x) = arcsin(1/x)~
