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:

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

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