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?

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?

amistre64 · Answer

the chain rule implies it by this problem yes.

dy        dy   du
--- = --- ----
dx        du   dx

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

perhaps :)

anonymous · Answer

thanks