Question

if h(x)=2g(x) - (1)/(g(x)) =2 and g'(0)=-1, find the exact value of h'(0). please please please help and show all steps!

Answer 1

what exactly is h?

h = 2g - (1/g); or
h = (2g - 1)/g
or something else?

Answer 2

h is 2g - (1/g)

Answer 3

Ok. So using the chain rule as I showed you earlier, what is h'?

dh/dx = dh/dg . dg/dx
= ... what?

Answer 4

okay is the answer 4?

Answer 5

what is g(0) equal to? is it the = 2 in your question?

Answer 6

yeah sorry g(0)=2

Answer 7

then the answer is not 4.

What's your expression for
h'(x)
?

Answer 8

h'(x)=2 + (g'(x)/(g(x)^2))

Answer 9

No.

dh/dx = dh/dg . dg/dx
= (2 + 1/g^2) g'

i.e.,
h'(x) = g'(x) [ 2 + 1/g(x)^2 ]

Answer 10

yes?

Answer 11

okay so is it -9/4?

Answer 12

Yes

Answer 13

okay thank you!