The Rules of Differentiation
Constant Rule
If f(x)=a and a is a real number, then
f′(x)=0.
Constant Multiple Rule
If f(x)=ax and a is a real number, then
f′(x)=a
Power Rule
If f(x)=xn and n is a real number, then
f′(x)=nxn−1.
Product Rule
If f and g are differentiable at x, then
(f∗g)′(x)=f(x)g′(x)+g(x)f′(x)
Quotient Rule
If f is the quotient h(x)g(x) and h(x)=0, then
f′(x)=[h(x)]2g′(x)h(x)−g(x)h′(x)
Chain Rule
If g is differentiable at x and f is differentiable at g(x), then
(f∘g)′(x)=f′(g(x))g′(x)