Calculus (3rd Edition)

$3x^{2}-6x-13$
The product rule when there are 3 operands is $(uvw)'=u'vw+uv'w+uvw'$ Therefore, $f'(x)=\frac{d}{dx}(x+3)\times(x-1)(x-5)+(x+3)\times\frac{d}{dx}(x-1)\times(x-5)+(x+3)(x-1)\frac{d}{dx}(x-5)$ $=1\times(x-1)(x-5)+(x+3)\times1\times(x-5)+(x+3)(x-1)\times1$ $=x^{2}-5x-x+5+x^{2}-5x+3x-15+x^{2}-x+3x-3$ $=3x^{2}-6x-13$