# CALCULUS - General Derivatives

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Added by Mitch Davis on November 01, 2001 at 01:55:45:

Given general functions U and V, variable X, and constant k and n

formal definition

lim [f(x+h) - f(x)] / h
h->0

General Rule:
f(X) = g(x) + h(x) + ...
dX[f(x)] = dx[g(x)] + dX[h(x)] + .....

with any given function, the derivative can be found be deriving its component functions (this rule is best used for polynomials)

Constant Rule:
dX[k] = 0

the derivative of any constant is 0

Power Rule:
dX[kX^n] = knX^(n-1)

basically, drop the power, mulitply by the constant, and reduce the power by 1

Product Rule:
dX[U*V] = dX[U]*V + U*dX[V]

Quotient Rule:
dX[U/V] = (dX[U]*V - U*dX[V])/(dX[V])^2

natural log:
ln(U) = dX[U] * (1/U)

Trig:
dX[sin(U)] = dX[U]cos(U)
dX[cos(U)] = -dX[U]sin(U)

these are the basic derivative rules which are used most, there are many more that can be found in calculus textbooks... if you have any questions or want to know if some rule for something exists, i will be pleased to respond to any emails