Therefore, we have

y $=$

$5$x$2+3$x $+3$

x

$=5$x$3/2+3$x$1/2+3$x$1/2.$

Now, since the function is a sum of power functions, we can use the Power Rule to find its derivative. Recall that according to the Power Rule, the derivative of

xn$,$

where n is any real number, is

nxn $1.$

To use the Power Rule, we'll have to calculate the following.

$32$

$1=$

$$

$12$

$1=$

$$

$12$

$1=$

Applying the Power Rule we have

y$\text{'}=$ x$1/2+$ x$1/2+$

x$3/2.$