Calculating Derivatives of Composite Functions

[kxpatel29]

Homework Statement

Given F(2)=5, F'(2)=6, F(4)=3, F'(4)=6 and G(3)=6, G'(3)=3, G(4)=2, G'(4)=1
A. H(4) if H(x)=F(G(x)) = ?
B. H'(4) if H(x)=F(G(x)) = ?
C. H(4) if H(x)=G(F(x)) = ?
D. H'(4) if H(x)=G(F(x)) =?
E. H'(4) if H(x)=F(x)/G(x) =?

Homework Equations

My teacher did not teach this yet, so I have no idea. My book doesn't even cover this

The Attempt at a Solution

Would we just use the given values? For E, F(x)/G(x)=1/2?

 

[Mark44]

Homework Statement

Given F(2)=5, F'(2)=6, F(4)=3, F'(4)=6 and G(3)=6, G'(3)=3, G(4)=2, G'(4)=1
A. H(4) if H(x)=F(G(x)) = ?
B. H'(4) if H(x)=F(G(x)) = ?
C. H(4) if H(x)=G(F(x)) = ?
D. H'(4) if H(x)=G(F(x)) =?
E. H'(4) if H(x)=F(x)/G(x) =?

Homework Equations

My teacher did not teach this yet, so I have no idea. My book doesn't even cover this

The Attempt at a Solution

Would we just use the given values? For E, F(x)/G(x)=1/2?

You have to use the given values, yes, but except for A and C, you need to take the derivative using either the chain rule (B and D) or quotient rule (E).

For example, if problem E were changed like so:
Given F(2)=5, F'(2)=6, F(4)=3, F'(4)=6 and G(3)=6, G'(3)=3, G(4)=2, G'(4)=1
Find H'(4) if H(x)=F(x)G(x)

then H'(4) = F(4)G'(4) + F'(4)G(4) = 3*1 + 6*2 = 3 + 12 = 15.
Here I have used the product rule.

Similar idea for all of them.