Chain rule combined with power rule (KristaKingMath)

People often think that chain rule has to be applied only in specific instances while taking the derivative. In fact, chain rule must always be applied, to every derivative. Sometimes applying chain rule just means multiplying by 1, which of course has no effect on the derivative, which is why it looks like chain rule is sometimes not applied.

Since chain rule is always applied, to every derivative, you'll very often have to use it in combination with power rule, product rule, or quotient rule. Power rule is the tool you use to take the derivative of power functions, and when the base of the power function is anything other than just "x", you must apply chain rule and multiply by the derivative of the base, which is the "inside" function. Remember that chain rule in general tells you to take the derivative of the outside function first, leaving the inside function completely untouched, and then to multiply your result by the derivative of the inside function.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[skipperpierce]

I have a calculus test tomorrow and have been desperately searching for somebody's explanation of these kinds of problems. you explained it so well, thank you so much

[donaldoji]

This girl is amazing! Nobody even comes close when it comes to explaining stuff clearly

[rohanmahajan]

Thank you mam you just made me learn chain rule so easily! All your video's are very helpful and make calculus easy to understand

[ruthandboys]

Thank you, as always. I really appreciate the step-by-step algebra. That's what trips me up.

[Utherful]

Power rule, Product Rule, Quotient Rule, Chain Rule, Are there any videos detailing where these rules come from, or should they just be memorised ?

[howawwe]

can you make a video on the product rule combined with the general power rule

[cowboyengineer]

hey! i have to tell you, i scoured the net and i could not find a good explanation of how to discern between the power rule and chain rule! but you've explained amazingly haha, even khan academy was not clear enough! thank you so much!!

[motijirata]

great video but how can I slove a problem when we have for instance :- x^sqrt2 ?

[valentinejepkemei]

Thank you much mom you explained it nicely💓

[cherryxx]

thanks a lot! you made it easier to understand than my math teacher!

[shubhamkannaujiya]

thank you very much. I am able to do derivatives .but unable to do integration please help