Given F (3) = 2, F' (3) = 6, F (4) = 2, F' (4) = 3 and G (2) = 7, G' (2) = 2, G (3)=4, G' (3)=4

Question

Given F (3) = 2, F' (3) = 6, F (4) = 2, F' (4) = 3

and G (2) = 7, G' (2) = 2, G (3)=4, G' (3)=4,

find each of the following.( Enter dne for any derivative that cannot be computed from this information alone.)

A) H (3) if H (x) = F( G(x) ) = ?

B) H' (3) if H (x) = F( G(x) ) = ?

C) H (3) if H (x) = G( F(x) ) = ?

D) H' (3) if H (x) = G( F(x) ) = ?

E) H' (3) if H (x) = F(x)/G(x) = ?

Answer 1

a) H(3) = F(G(3)) = F(4) = 2

b) H'(3) (using the chain rule) = F'(G(3))•G'(3) = F'(4)•4 = 3•4 = 12

c) H(3) = G(F(3)) = G(2) = 7

d) H'(3) (using the chain rule) = G'(F(3))•F'(3) = G'(2)•6 = 2•6 = 12

e) H'(3) (using the quotient rule) = [F'(3)•G(3) - F(3)G'(3)]/(G(3))² = (6•4 - 2•4)/4² = (24 - 8)/16 = 16/16 = 1

Answer 2

H(3) = F(G(3)) = F(4) = 2

By the Chain Rule, H'(3) = F'(G(3))G'(3) = F'(4)G'(3) = (3)(4) = 12

ETC