Find the Derivative

[oriont]

y=(9+4x-8 sqrt x)/x

Using the quotient rule I get

[x(4-4x^-1/2)-(9+4x-8x^1/2)]x^2

[4x-(4x^1/2)-9-4x+(8x^1/2)]x^2

[(8x^1/2)-9]x^2

My final answer is (4sqrtx-9)/x^2

However the boosk final answer is

-9/x^2 + 4/xsqrtx

It has been a year since I took trig and I know my algebra is horrible but how did they get 4/xsqrtx from 4sqrtx/x^2

Thanks for the help.

 

[Deleted member 4993]

y=(9+4x-8 sqrt x)/x

Using the quotient rule I get

[x(4-4x^-1/2)-(9+4x-8x^1/2)]x^2

[4x-(4x^1/2)-9-4x+(8x^1/2)]x^2

[(8x^1/2)-9]x^2

My final answer is (4sqrtx-9)/x^2

However the boosk final answer is

-9/x^2 + 4/xsqrtx

It has been a year since I took trig and I know my algebra is horrible but how did they get 4/xsqrtx from 4sqrtx/x^2

Thanks for the help.

\(\displaystyle \dfrac{4\sqrt{x}}{x^2} \ = \ \dfrac{4\sqrt{x}}{x*x} \ = \ \dfrac{4\sqrt{x}}{\sqrt{x}\sqrt{x}*x}\)

Now get rid of one \(\displaystyle \sqrt{x}\) each from the denominator and the numerator.

 

[oriont]

Appreciate the answer, thanks all.