Given y=u^2-1/2u+1 and u=-2x^3+3x, find dy/dx

[ttpp1124]

Homework Statement

Question and answer are two separate images...I feel like some steps can be removed..?
Can someone check my work?

Relevant Equations

n/a

 

[Mark44]

The image you posted is mostly unreadable. The leftmost two-thirds are in shadow, and the page isn't flat, making the problem worse.
Please post a more readable image of your work, with the paper better lit and flatter.

 

[Eclair_de_XII]

Looks correct to me.

Given: $y(u)=\frac{u^2-1}{2u+1}$ where $u=u(x)=-2x^3+3x$
===
$y'(u)=\frac{(2u)(2u+1)-(u^2-1)(2)}{(2u+1)^2}=\frac{4u^2+2u-2u^2+2}{(2u+1)^2}=\frac{2u^2+2u+2}{(2u+1)^2}=2\cdot \frac{u^2+u+1}{(2u+1)^2}$
$u'(x)=-6x^2+3$
===
$u(2)=-2(2)^3+3(2)=-16+6=-10$
===
$y'(u(2))=2\cdot \frac{100-10+1}{(-20+1)^2}=2(\frac{91}{19^2})$
$u'(2)=-6(2)^2+3=-21$
===

Hence, $(y\circ u)'(2)=y'(u(2))u'(2)=2(\frac{91}{361})(-21)=\frac{-42\cdot 91}{19\cdot 19}$, as you have written in your paper.

 

[epenguin]

The image you posted is mostly unreadable. The leftmost two-thirds are in shadow, and the page isn't flat, making the problem worse.
Please post a more readable image of your work, with the paper better lit and flatter.

As you are making a habit of only just about readable photos, I recommend you clean them with an app such as DocHD.
Then worse than irritating is the title, which everyone suspects is wrong as soon as they see it. This is confirmed as soon as they read the post which states the formula we thought probably meant, but it's a dangerous habit.