The Product Rule states that if you have two functions u(x) and v(x), the derivative of their product is given by: (uv)' = u'v + uv'.

The Quotient Rule states that if you have two functions u(x) and v(x), the derivative of their quotient is given by: (u/v)' = (u'v - uv') / v^2.

To differentiate a function using the Product Rule, identify the two functions being multiplied, find their derivatives, and apply the formula: (uv)' = u'v + uv'.

To differentiate a function using the Quotient Rule, identify the numerator and denominator functions, find their derivatives, and apply the formula: (u/v)' = (u'v - uv') / v^2.

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

To determine where a function is increasing or decreasing, find the derivative of the function, set it to zero to find critical points, and analyze the sign of the derivative in the intervals defined by these points.