Find the derivative of the following function without using the product rule,

f$($x$)=7$x$($x$311$x$2+4$x$+4)$

First, rewrite the function in an equivalent way so that the product rule need not be applied,

f$($x$)=$

x$37$x$11$x$27$x$+4$x$7$x$+47$x

$.$

Now, compute the derivative,

f$\text{'}($x$)=$

$(3$x$2+$x$322$x$+4)7$xln$(7)$

$.$