How do you use the chain rule to differentiate #y=(x+1)^3#?

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Answer 1 · 2018-05-07T20:18:30

#=3(x+1)^2#

#y=u^2#

where #u=(x+1)#

#y'=3u^2*u'#

#u' = 1#

#y'=3(x+1)^2#

Answer 2 · 2018-05-08T01:54:39

#3(x+1)^2#

The chain rule states that,

#dy/dx=dy/(du)*(du)/dx#

Let #u=x+1,:.(du)/dx=1#.

Then #y=u^3,:.dy/(du)=3u^2# by the chain rule.

So combining, we get,

#dy/dx=3u^2*1#

#=3u^2#

Substituting back #u=x+1#, we get the final answer:

#color(blue)(bar(ul(|3(x+1)^2|)#