CK12 Calculus - Single Variable

Keepin mindthat

Example7:

Find for
Solution:
Thereare two methodsto solvethis problem.One is to multiplythe productand then use the derivativeof
the sum rule. The secondis to directlyuse the productrule. Eitherrule will producethe sameanswer. We
beginwith the sum rule.

Takingthe derivativeof the sum yields

Now we use the productrule,

whichis the sameanswer.

The QuotientRuleIffandgare differentiablefunctionsatxandg(x) ≠ 0, then

In simplernotation,

The derivativeof a quotientof two functionsis the

bottomtimesthe derivativeof the top minusthe top timesthe derivativeof the

bottomall over the bottomsquared.

Keepin mindthat the orderof operationsis important(becauseof the minussign in the numerator)and