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C3 Chain rule question

Is the chain rule only valid for linear functions? I always thought it was but then I came across a function where it wasn't linear but the chain rule was used
Reply 1
Avatar for NR22
NR22
12
What do you mean by you thought it was only linear? Do you mean you didn’t think you would use the chain rule on say (quadratic equation)^n to get n(quadratic equation)^(n-1) *(differential of quadratic equation)
Reply 2
Avatar for Uvuwewewe
Uvuwewewe
OP
10
Original post by NR22
What do you mean by you thought it was only linear? Do you mean you didn’t think you would use the chain rule on say (quadratic equation)^n to get n(quadratic equation)^(n-1) *(differential of quadratic equation)


Yeah, so can you use it for all non linear equations such the one you gave?
Reply 3
Avatar for MCArth
MCArth
9
It is valid for everything you can sub u in for. However, be careful not to get confused about reverse chain rule on integration questions, which IS only valid for linear functions.
Reply 4
Avatar for NR22
NR22
12
Original post by Uvuwewewe
Yeah, so can you use it for all non linear equations such the one you gave?


Yes you can use the chain rule for all non linear equations just like the one I gave you, you might use it on trig as-well don’t forget that either, may help you out!
Original post by Uvuwewewe
Yeah, so can you use it for all non linear equations such the one you gave?


Original post by NR22
Yes you can use the chain rule for all non linear equations just like the one I gave you, you might use it on trig as-well don’t forget that either, may help you out!


The chain rule is valid for any composition of differentiable functions - equation is the wrong word. Make sure you understand the difference: see https://math.stackexchange.com/questions/1603753/difference-between-function-and-equation.
Reply 6
Avatar for Uvuwewewe
Uvuwewewe
OP
10
Original post by MCArth
It is valid for everything you can sub u in for. However, be careful not to get confused about reverse chain rule on integration questions, which IS only valid for linear functions.


Ah yes, that's probably where I got my assumption from. I haven't revised C3 in a while so it's still a bit of a blur, thanks for the reminder
Reply 7
Avatar for Uvuwewewe
Uvuwewewe
OP
10
Original post by NR22
Yes you can use the chain rule for all non linear equations just like the one I gave you, you might use it on trig as-well don’t forget that either, may help you out!


Okay, thanks!

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