Given the following functions: F(u)= u^(5/2) and g(x)= x^6+1, find-f(g(x))=?, f'(u)=?, f'(g(x))=?, g'(x)=?,(f o g)'(x)=?

Answer 1

f(g) = (fog) = g^(5/2) = (x^6 + 1)^(5/2)

f'(u) = /2 u^(3/2)

f'(g(x)) = 5/2 g^(3/2) g' = 5/2 (x^6+1)^(3/2) * 6x^5

g'(x) = 6x^5

(fog)' = 5/2 (x^6+1)^(3/2) * 6x^5