I am having problems solving the following question.
Let $F(x)=h(g(f(x))),$ where $f(2)=4, g(4)=4, f\prime(2)=3 , g\prime(4)=6 , $and $h\prime(4)=10$
Then $F\prime(2)$ equals. . .
I am assuming I am to use the Chain rule but am uncertain on how to use the Chain rule without given a function with variables.
Given $f(x) = (3x^2 + 4x)^2 \\ f`(x)g(x)g`(x) \\ 2(3x^2 + 4x)(6x+4)$
What I currently think the solution is, is:
$F\prime(2) = h\prime(g(x)*g\prime(x))\\ = h\prime(g\prime(f(x)*f\prime(x))g\prime(x))\\=4320$
But this is clearly not the correct solution. Please inform me where I have made a mistake.
Thank you,