So Lost

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Let H(x)=F(G(x)) and J(x)=F(x)/G(x). Suppose
F(7)=8, F?(7)=1
G(7)=3, G?(7)=?1
G(3)=7, G?(3)=1
then
H(3)=
H?(3)=
J(7)=
J?(7)=

 

[mmm4444bot]

Chain Rule

Quotient Rule (or Product Rule, if you prefer to factor first)

They've given values for the required parts.

Substitute and do the arithmetic.

I'll do H(3). You make an effort on the rest.

H(x) = F( G[x] )

Chain rule says:

H'(x) = F'(G[x]) * G'(x)

They give values for all of the needed parts, when x = 3.

G[3] = 7

So F'(G[3]) = F'(7), which is given as 1.

Also, G'(3) is given as 1.

Substitution into the Product Rule gives:

H'(3) = 1 * 1