Question

find the derivative of the function
y = (1-2sqrt(x))/(1-2xsqrt(x)) find the derivative of the function
y = (1-2sqrt(x))/(1-2xsqrt(x)) @Mathematics

Answer 1

y' = (1-2X^1/2)(1-2XsqrtX) - (1-2x^3/2)(1-2sqrtX) all over (1-2x^3/2)^2

Answer 2

thats what i got so far

Answer 3

\[\frac{1-2\sqrt{x}}{1-2x\sqrt{x}}\]?

Answer 4

yes

Answer 5

that gives one butt ugly derivative for sure .

Answer 6

you need all the algebra, or the answer? because even "simplified" it is not that "simple"

Answer 7

lol i have the answer but i need to know how to get to it

Answer 8

you need all the algebra, or the answer? because even "simplified" it is not that "simple"

Answer 9

lorda mercy. looks like you have the first step.
\[(\frac{f}{g})'=\frac{gf'-fg'}{g^2}\] now i would like to make life a little simpler by writing
\[\frac{2\sqrt{x}-1}{2x\sqrt{x}-1}\] and then put
\[f(x)=2\sqrt{x}-1, f'(x)=\frac{1}{\sqrt{x}}\]
\[g(x)=2x\sqrt{x}-1,f'(x)=3\sqrt{x}\]

Answer 10

plugging all this mess in to the "quotient rule" gives
\[\frac{(2x\sqrt{x}-1)\times \frac{1}{\sqrt{x}}-(2\sqrt{x}-1)\times 3\sqrt{x}}{(2x\sqrt{x}-1)^2}\]

Answer 11

now probably best bet is to get rid of the compound fraction by multiplying top and bottom by
\[\sqrt{x}\] so give
\[\frac{(2x\sqrt{x}-1)-(2\sqrt{x}-1)\times 3x}{\sqrt{x}(2x\sqrt{x}-1)^2}\]

Answer 12

then some more algebra in the numerator, which i will get you finish because i will probably mess it up

Answer 13

ok i will try thanks

Answer 14

you need all the algebra, or the answer? because even "simplified" it is not that "simple"

Answer 15

yw. just multiply out and it should be good. or course i mean in the numerator. leave the denominator alone. if you have the answer you know what you are working towards, and i think i didn't screw up the first part

Answer 16

but isnt the derivative of 1-2sqrt(x) = -1/sqrt(x)