Question

If y=2sqrt(x)-(1/2sqrt(x)), then what is the derivative of y with respect to x?

Answer 1

square root means power of a half
\[\sqrt{x}=x^{\frac{ 1 }{ 2 }}\]

Answer 2

\[\frac{ 1 }{ 2\sqrt{x} }= \frac{ 1 }{ 2}\frac{ 1 }{ \sqrt{x} }\]
\[\frac{ 1 }{ a}=a^{-1}\]

Answer 3

so you end up re writing your equation to be
\[y=2x^{\frac{ 1 }{ 2 }} - \frac{ x^{-\frac{ 1 }{ 2 }} }{ 2 }\]

Answer 4

now you can differentiate this using
\[\frac{ dy }{ dx }=nx^{n-1}\] where n is the power

Answer 5

give it a go and I will correct you if you go wrong