Question

Please help with a Calc problem!!

Answer 1

Ok since we need to take the derivative with respect to u we need to replace the x in our equation in terms of u
We are told that \(u=2x-1\) so \(x=\frac{1}{2}(u+1)\)
So now lets replace x in terms of u
\[y=x^2+2\]
\[y=\left(\frac{1}{2}(u+1)\right)^2+2\]
\[y=\frac{1}{4}(u^2+2u+1)+2\]
\[y=\frac{1}{4}u^2+\frac{1}{2}u+\frac{9}{4}\]

Now we take the derivative with respect to u
\[\frac{dy}{du}\{\frac{1}{4}u^2+\frac{1}{2}u+\frac{9}{4}\}\]
\[\frac{dy}{du} \{ \frac{1}{4}u^2\}+\frac{dy}{du}\{\frac{1}{2}u \} +\frac{dy}{du}\{\frac{9}{4}\}\]
\[=\frac{1}{2}u+\frac{1}{2}+0\]

Answer 2

Thank you so much for taking the time to write out that response! I'm still a little confused because my teacher told me that the answer is \[6x ^{2}-2x+4\] I don't understand how she came to that answer.

Answer 3

hmmmm i bet he replaced the u with the x's again
Wait lemme just write it out and see if it works out

Answer 4

hmmm doesnt work out hmmm

Answer 5

Yeah. I'm kinda confused. Maybe my teacher has the wrong answer?

Answer 6

@ganeshie8 where am I going wrong??

Answer 7

Its impossible for the derivative to be a quadratic equation since the original equation is quadratic

Answer 8

im getting the same as yours

Answer 9

yeah

Answer 10

Ok lets assume that your teacher accidentally supplied the incorrect answer

Answer 11

Thank you so much! I really appreciate you taking the time to help. :)

Answer 12

np :)