$Iffis$ a differentiable function, find $an$ expression for the

derivative $of$ each $of$ the following functions:

$In$ submitting the answers below, write $f(x)asf,$ and write

$f^{\text{'}}(x)asg.$

$(a)Ify=x^{2}f(x),$ then $y^{\text{'}}=g{x}^2+f2x$

$(b)Ify=\frac{f(x)}{x^2},$ then $y^{\text{'}}=\frac{g{x}^2-f2x}{x^4}$

$(c)Ify=\frac{x^2}{f(x)},$ then $y^{\text{'}}=\frac{2xf-x^{2}g}{f^2}$

$(d)Ify=\frac{1+xf(x)}{\sqrt[\phantom{2}]{x}},$ then $y^{\text{'}}=\frac{g\sqrt[\phantom{2}]{x}-\frac{1+xf}{2\sqrt[\phantom{2}]{x}}}{x}$