Derivatives
d/dx(ex)=
what ex?
d/dx(uv)=
Product Rule
u(dv/dx)+v(du/dx)
d/dx(sin(x))=
what cos(x)?
d/dx(sin-1(x))=
1/(1-x2)1/2
d/dx(xn)=
what is nxn-1?
d/dx(u/v)=
Quotient Rule
(du/dx)(v)-(u)(dv/dx)
--------------------------
v2
d/dx(cos(x))=
-sin(x)
d/dx(cos-1(x))=
-1/(1-x2)1/2
d/dx (In(x))=
what is 1/x?
Define Mean Value Theorem including constraints, and formula.
If the function f is continuous on [a,b] and the first derivative exists on the interval, then there exists a number c, where
f(b)-f(a)
f'(c)= -------------------
b-a
d/dx(tan(x))=
sec2(x)
d/dx(tan-1(x))=
1/(1+x2)
d/dx(ax)=
axIn(a)
Disk Method
pi(integral from a to b)[R(x)2]dx
d/dx(sec(x))=
sec(x)tan(x)
d/dx(cot-1(x))=
-1/(1+x2)
d/dx(loga(x))=
-1/xIn(a)
Washer Method
pi(integral from a to b)([R(x)]2-[r(x)]2)dx
d/dx(cot(x))=
-csc2(x)
d/dx(sec-1(x))=
1/(|x|(x2-1)1/2)