Calculus (3rd Edition)

Given: $f(u)=u^{3}$, $g(x)=3x+5$ We find the composite function as follows: $f(g(x))=(3x+5)^{3}$ Now, take the derivatives: $f'(u)= 3u^{3-1}=3u^{2}$ $f'(g(x))=3(3x+5)^{2}$ $g'(x)=3$ $(f\circ g)'=f'(g(x))\times g'(x)$ $=3(3x+5)^{2}\times3=9(3x+5)^{2}$ See the filled table below.