Question

If y = (u-3)/ (u+3) and u = 8/ sqrt (x) , use the chain rule to find dy /dx when x =4

Answer 1

\[\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}\]
\[y = \frac{u-3}{u+3}\] so you need the quotient rule for this one, get
\[\frac{dy}{du}=\frac{6}{(u+3)^2}\]

Answer 2

\[u=\frac{8}{\sqrt{x}}\]
\[\frac{du}{dx}=\frac{-4}{\sqrt{x^3}}\]

Answer 3

multiply them together to get your answer, get
\[\frac{dy}{dx}=\frac{6}{(u+3)^2}\times \frac{-4}{\sqrt{x^3}}\]

Answer 4

and finally replace y by
\[\frac{8}{\sqrt{x}}\]

Answer 5

*replace u, not y

Answer 6

srry where does the -4 / sqrt (x^3) from?

Answer 7

oh and it said when x = 4!!

Answer 8

so replace x by 4, or do it before multiplying

Answer 9

\[\frac{8}{\sqrt{x}}=8x^{-\frac{1}{2}}\]
now power rule

Answer 10

get
\[-4x^{-\frac{3}{2}}=\frac{-4}{\sqrt{x^3}}\]

Answer 11

ohh ok i get it thanks!

Answer 12

we can do this easier if we let x = 4 earlier on

Answer 13

x = 4,
\[\frac{8}{\sqrt{4}}=\frac{8}{2}=4\] so we can replace u by 4 in the derivative and get
\[\frac{dy}{du}=\frac{6}{(4+3)^2}\]

Answer 14

but it is not necessary

Answer 15

oh ok thanks for your help :)