Tutorial Exercise

Find the derivative of the function.

$y=\frac{1}{2}[x\sqrt[\phantom{2}]{9-x^2}+9arcsin(\frac{x}{3})]$

Step $1$

Rewrite the given function $y=\frac{1}{2}[x\sqrt[\phantom{2}]{9-x^2}+9arcsin(\frac{x}{3})]$ as

$y=\frac{1}{2}[x(,{)}^{\frac{1}{2}}+9arcsin(\frac{x}{3})]$