Question

Can anyone explain on how to use the chain rule for this equation?

Answer 1

\[y=2u^2-u+5\] and
\[u=1-x^2\] so by the "chain of relations" you can write \(y\) in terms of \(x\) as
\[y=2(1-x^2)^2-(1-x^2)+5\]

Answer 2

you can so some algebra if you like
now you are asked for
\[\frac{dy}{dx}\] which you can compute via
\[\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\]

Answer 3

\[y=2u^2-u+5\] gives
\[\frac{dy}{du}=4u-1\] and of course \[\frac{du}{dx}=-2x\] so you get
\[\frac{dy}{dx}=(4u-1)(-2x)\]

Answer 4

now if you want the answer only in terms of \(x\) replace \(u\) b y \(1-x^2\) and you will get it

Answer 5

Thank You :)