Question

Use the chain rule to find dy/dx for the given value of x.

y= (u-1/u+1)^1/2

u= sqrt x-1; for x= 34/9

I got to 1/2 (u-1/u+1)^-1/2. Do I need to do quotient rule also?

Answer 1

the chain rule implies it by this problem yes.

dy dy du
--- = --- ----
dx du dx

Answer 2

so after the step that I have, do the quotient rule next

Answer 3

y = m^2 ; dy/dm = 2m

m = (u-1/u+1); dm/du = derivative rule

u = sqrt(x-1) ; du/dx = 1/2sqrt(x-1)

dy/dx = dy/dm * dm/du * du/dx

Answer 4

opps y = m^(1/2); dy/dm = 1/2sqrt(m)

Answer 5

\[\frac{1}{2(\frac{\sqrt{x-1}+1}{\sqrt{x-1}-1})} * \frac{(\sqrt{x-1}+1)(\frac{1}{2 \sqrt{x-1}})-(\sqrt{x-1}-1)(\frac{1}{2 \sqrt{x-1}})}{(\sqrt{x-1}+1)^2} * \frac{1}{2 \sqrt{x-1}}\]

Answer 6

perhaps :)

Answer 7

thanks