Question

use the chain rule to find dy/dx given y=2u/u^2-1 ,u=x^2

Answer 1

\[\Large\rm y=\frac{2u}{u^2-1}\]So I guess uhh, start with the quotient rule.\[\Large\rm y'=\frac{(2u)'(u^2-1)-(2u)(u^2-1)'}{(u^2-1)^2}\]

Answer 2

\(\Huge\bf \color{yellow}{Welcome~to~OpenStudy!!}\hspace{-310pt}\color{cyan}{Welcome~to~OpenStudy!!}\hspace{-307.1pt}\color{midnightblue}{Welcome~to~\color{purple}{Open}}\color{blue}{Study!!!!}\)

Answer 3

oo that's pretty =o

Answer 4

\[\Large\rm y'=\frac{(2)u'(u^2-1)-(2u)(u^2-1)'}{(u^2-1)^2}\]For this first term, derivative of 2u gives us 2,
chain rule tells us to multiply by the derivative of u.

Answer 5

So if \(\Large\rm u=x^2\)
Our derivative with respect to u is,\[\Large\rm u'=2x\]Yes?

Answer 6

with respect to x*

Answer 7

Yep. It's really pretty:D