Question

Find the derivative of y= cos^2 ( 1-sqrt (x) / 1+ sqrt (x) )

Answer 1

can someone show me the steps to get it
i really dont know what i did wrong

Answer 2

first step would be power rule..so 2cos(1 - sqrtx/1+ sqrt x)

then take the derivative of cos so..

2cos(1 - sqrtx/1+sqrt)sin(1-sqrtx/1+sqrtx)

then take the derivative of 1 - sqrtx/1+sqrtx...do you know how?

Answer 3

what i dont know how to do is the 1- sqrt x / 1+sqrt x one...

Answer 4

cuz my answer is - 1 + sqrt x - 1 - sqrt x / 2 sqrt x

Answer 5

the final answer given is sin 2 ( 1- sqrt (x) / 1+ sqrt (x) ) ( 1 / sqrt x ( 1+ sqrt x) ^2

Answer 6

so my answer does not seem to be right

Answer 7

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

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

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

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

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

\(\Huge \frac{\frac{-1}{\sqrt x} }{(1+ 2\sqrt x + x)}\)

\(\Huge \frac{-1}{\sqrt x(1+ 2\sqrt x + x)}\)

\(\Huge \frac{-1}{\sqrt x + 2x + x\sqrt x)}\)

that's what i got