(1 point) let ( r ( x ) = f ( g ( h ( x ) ) ) ), where ( h ( 1 ) = 2 ), ( g ( 2 ) = 3 ), ( h ^ { prime } ( 1…

Explanation:

Step1: Apply the chain rule

The chain rule states that if (r(x)=f(g(h(x)))), then (r^{\prime}(x)=f^{\prime}(g(h(x)))\cdot g^{\prime}(h(x))\cdot h^{\prime}(x)).

Step2: Substitute (x = 1)

When (x = 1), we have: (r^{\prime}(1)=f^{\prime}(g(h(1)))\cdot g^{\prime}(h(1))\cdot h^{\prime}(1)) Since (h(1) = 2), then (r^{\prime}(1)=f^{\prime}(g(2))\cdot g^{\prime}(2)\cdot h^{\prime}(1))

Step3: Substitute known values

Given (g(2)=3), (g^{\prime}(2) = 5), (h^{\prime}(1)=4), and (f^{\prime}(3)=6) (r^{\prime}(1)=f^{\prime}(3)\cdot5\cdot4) (r^{\prime}(1)=6\times5\times4) (r^{\prime}(1)=120)

Answer:

(120)