The [[derivative]] of the product of two functions $f(x)$ and $g(x)$ can be calculated as the first function times the derivative of the second function plus the derivative of the first function times the second function
$(f*g)' = f*g' + f'*g$
From the product rule we can show that the derivative of a constant times a function is the constant times the derivative of the function. Notice that the second term in the above equation will be 0 since the [[derivative of a constant]] is 0.
$f'(cx) = cf'(x)$