Question

suppose f(1)=3, f'(1)=2, g(2)=2, g'(2)=8, h(x)=g(2x), and F(x)=f(x)/g(2x).

find h'(1) and F'(1)

Answer 1

we use the quotient rule for F'(1) i think but how do we get h'(1)

Answer 2

Hello

Answer 3

Hi

Answer 4

So for the first question, by the chain rule, what is the derivative of h(x)?

Answer 5

h(x)=g(2x)
hence
h'(x) = ... what?

Answer 6

2g'(2x)

Answer 7

Right, hence
h'(1) = 2g'(2) = ...

Answer 8

still there?

Answer 9

always

Answer 10

im trying to do it on paper

Answer 11

Remember what you're told:
f(1)=3, f'(1)=2, g(2)=2, g'(2)=8

Now, as h'(x) = 2g'(2x)
h'(1) = 2g'(2) = ... what?

Answer 12

2 times 8 = 16

Answer 13

Right.

Now part b. Use the quotient rule:
F'(x) = ...

Answer 14

-11?

Answer 15

Looks about right

Answer 16

might need more help with a different problem so be on the lookout lols