## anonymous 5 years ago 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?

1. amistre64

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

2. anonymous

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

3. amistre64

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

4. amistre64

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

5. amistre64

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

6. amistre64

perhaps :)

7. anonymous

thanks