Question

y(x)=f(x+g(x))
Find y'(0)
if: f'(1)=1/3
g(0)=1
g'(0)=1/3
can anybody help with this please, I am nearly tearing my hair out, thanks

Answer 1

Well, don't go bald yet. :)

Answer 2

Your first step should probably me to use the chain rule. Have you tried that?

Answer 3

so f'(x+g(x)).(1+g'(x))?

Answer 4

good!

Answer 5

Now, using the given information what do you get?

Answer 6

haha give me a moment just thinking

Answer 7

no worries, take your time. :)

Answer 8

f'((1))+g(0)).(1+g'(0))
=(-1/3+1).(1+1/3)?

Answer 9

close... you should plug in a 0 for all x's (you have a 1 that appears in the first part). We are evaluating y'(0) so x = 0.

Answer 10

\[y'(0) = f'(0 + g(0)) \cdot (1 + g'(0))\]

Answer 11

Does that make sense?

Answer 12

ah yes ok :)

Answer 13

cool, you are close to slaying this dragon. :)

Answer 14

so then:
f'(0+1).(1+1/3)
=f'(1).(1+1/3)
=-1/3.(1+1/3)?

Answer 15

In your OP you said that f'(1) = 1/3 positive, but if it should have been negative then yes. :)

Answer 16

yes sorry it should have been -1/3

Answer 17

Then, you are correct!

Answer 18

thank you so very very much :)

Answer 19

no worries, and now you can keep your hair. :)

Answer 20

haha yes :)

Answer 21

take care! nice work!

Answer 22

awww thanks :), you take care too :)