Question 1189629


given:

{{{f(u)= u/ (u^2-1) }}}
{{{u=g(x)=6x^2+x+4}}}
{{{x=0}}}

Find: the value of (f ∘ g)′ at the given value of {{{x}}}.

(f ∘ g)′ ={{{f(g(x))}}}

(f ∘ g)′ ={{{f(6x^2+x+4)}}}

(f ∘ g)′ ={{{(6x^2+x+4)/((6x^2+x+4)^2-1)}}}

(f ∘ g)′ ={{{(6x^2+x+4)/((6 x^2 + x + 3) (6 x^2 + x + 5))}}}

substitute {{{x=0}}}

(f ∘ g)′{{{(0) =(6*0^2+0+4)/((6 *0^2 + 0 + 3) (6 *0^2 + 0 + 5))}}}

(f ∘ g)′{{{(0) =4/( 3* 5)}}}

(f ∘ g)′{{{(0) =4/15}}}