The primary operation in differential calculus is finding a derivative. This table lists derivatives of many functions. In the following, f and g are functions of x, and c is a constant. The set of real numbers is assumed. These formulas are sufficient to differentiate any elementary function.
Definitions of the
Derivative:
df / dx = lim (dx -> 0) (f(x+dx) - f(x)) / dx
(right sided)
df / dx = lim (dx ->
0) (f(x) - f(x-dx)) / dx (left
sided)
df / dx = lim (dx -> 0) (f(x+dx) - f(x-dx)) /
(2dx) (both sided)
   f(t) dt = f(x) (Fundamental Theorem
for Derivatives)
c f(x) = c
f(x) (c is a constant)
(f(x) + g(x)) = f(x) +
g(x)
f(g(x)) =  f(g) *
g(x) (chain rule)
f(x)g(x) = f'(x)g(x) + f(x)g '(x) (product rule)
f(x)/g(x) =
( f '(x)g(x) - f(x)g '(x) ) / g2(x) (quotient rule)
Partial Differentiation Identities
if f( x(r,s), y(r,s) )
df / dr = df / dx * dx / DR + df / dy * dy / DR
df / ds = df / dx * dx / Ds + df / dy * dy / Ds
if f( x(r,s) )
df / DR = df / dx * dx / DR
df / Ds = df / dx * dx / Ds
directional derivative
df(x,y) / d(Xi sub a) = f1(x,y) cos(a) + f2(x,y) sin(a)
(Xi sub a) = angle counterclockwise from pos. x axis.
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