## anonymous 4 years ago find d^2y/dx^2 for y=(1-x)/(2-x)

1. amistre64

find the second derivative ... right?

2. anonymous

yes

3. anonymous

try the quotient rule

4. amistre64

then i would either use a product rule with a ^-1; or the quotient rule

5. anonymous

ok thanks so much

6. amistre64

youd have to do it twice tho to get to the second one

7. anonymous

ok

8. amistre64

$\frac{t}{b}=tb^{-1}$ $D_x[tb^{-1}]=-tb^{-2}+t'b^{-1}$ $D_{x}^{2}[tb^{-1}]=D_x[-tb^{-2}+t'b^{-1}]$ $D_x[-tb^{-2}+b^{-1}]=2tb^{-3}-t'b^{-2}-t'b^{-2}+t''b^{-1}$ witha any luck I kept it all in order lol

9. amistre64

t=(1-x) t' = -1 t'' = 0 b=(2-x) $2(1-x)(2-x)^{-3}+(2-x)^{-2}+(2-x)^{-2}+0(b^{-1})$ $2(1-x)(2-x)^{-3}+2(2-x)^{-2}$ $2(2-x)^{-3}\left((1-x)+(2-x)\right)$ $\frac{2(3)}{(2-x)^{3}}$ the wolf should be able to check that tho