Question

Find the derivative of the function.
r(x) = (e^6x-1)^8

I am having a hard time understanding derivatives in my Calculus class right now. I would very much appreciate if someone could help me solve this problem. It's one of the ones I'm stuck on at the moment. =(

Answer 1

chain. rule.

Answer 2

you should first use the one of the Chain Rule--General Power Rule:
d/dx [u^n]=nu^(n-1)u'
set (e^6x-1) as u, so you will get:
r(x)=u^8
then you apply the power rule to it, you will get:
r'(x)=8u^7u'
so what is u' ?
u'=d/dx [e^6x-1]
the derivative of e^(6x)-1 is 6e^(6x) because d/dx [e^u] = u' e^u
now you can get the answer:
r'(x)=8(e^6x-1)^7(6e^(6x))

Answer 3

wow ty so much cc, your answer was so very helpful, and explained it all perfectly!! ty<3

Answer 4

you are welcome~ enjoy your calculus :3