Consider the product of two simple functions, say {{MATH_8}} where {{MATH_9}} and {{MATH_10}}. An obvious guess for the derivative of {{MATH_11}} is the product of the derivatives: {{ENV_12}} Is this guess correct? We can check by rewriting {{MATH_13}} and {{MATH_14}} and doing the calculation in a way that is known to work. Write with me {{ENV_15}} Hence {{MATH_16}} so we see that {{MATH_17}} So the derivative of {{MATH_18}} is {{CMD_19}}not{{CMD_20}} as simple as {{MATH_21}}. Never fear, we have a rule for exactly this situation.