Okay, guys, I have two questions this time:

1. If $\displaystyle f(x) = {({\sqrt{{4x}^{2 } - 3 })^{\frac{-1}{2}$ then how does it become $\displaystyle f(x) = ({x}^{2} -3)^{\frac{1}{2}} $? Shouldn't it become $\displaystyle f(x) =((4x-3)^{\frac{1}{2}})^{\frac{-1}{2}}$? My book did the in one step, before differentiating. The solution really threw me off.

2. Is the derivative of $\displaystyle f(x) = (cos{x}^{2})$ $\displaystyle f'(x) = (-2sinx)$ or $\displaystyle (-sin{x}^{2}) · (2x)$? Is the $\displaystyle {x}^{2}$ a separate term and thus differentiated separately? If that is the case, would I use the same convention to deal with $\displaystyle f(x) = {sin}^{2}x$?

Thanks in advance guys for all the help.