Question

{a^(1/2)+x^(1/2)}/{a^(1/2)-x^(1/2)}
Find dy/dx.

Answer 1

\[(a^{.5}+x^{.5})~(a^{.5}-x^{.5})^{-1}\]
use the product rule

Answer 2

a^.5 is just some constant .... let it be 3 if need be

Answer 3

\[([3]+x^{.5})~([3]-x^{.5})^{-1}\]
\[([3]+x^{.5})'~([3]-x^{.5})^{-1}+([3]+x^{.5})~([3]-x^{.5})'^{-1}\]
\[\frac{1}{2x^{.5}}'~([3]-x^{.5})^{-1}+([3]+x^{.5})~([3]-x^{.5})'^{-1}\]
\[\frac{1}{2x^{.5}}'~([3]-x^{.5})^{-1}-\frac{1}{2x^{.5}}([3]+x^{.5})~([3]-x^{.5})^{-2}\]

Answer 4

got a spurious little ' that i didnt edit

Answer 5

and i forgot the - from the last one ....

\[\frac{1}{2x^{.5}}~([3]-x^{.5})^{-1}+\frac{1}{2x^{.5}}([3]+x^{.5})~([3]-x^{.5})^{-2}\]