Question

suppose that f(4)=3 and f ' (4)=-5. Find g ' (4) where g(x)=√x f(x).

Answer 1

find dg/dx
then put in those values

Answer 2

but how find dg/dx ?

Answer 3

for this =√x f(x).

Answer 4

yes

Answer 5

okey how ?!

Answer 6

do u know the product rule?

Answer 7

I know that but what mean this f(x) in √x f(x). ?

Answer 8

its just a function ... the value for it is defined in the given statement so just derive g

Answer 9

the function g, is composed of the product of the function sqrt(x), and the function f(x)

apply the product rule ....

Answer 10

=1/2(x)^-1/2 . f(x) + (x)^1/2 . ?

Answer 11

what is the derivative of f(x) ??

Answer 12

=1 ?

Answer 13

BRB I come back >

Answer 14

no .. would you agree that the derivative of g(x) ... is g'(x) ??

if so, the what is the derivative of f(x) notate out to be?

Answer 15

y derives to y'
g derives to g'
h derives to h'
f derives to ____ ???

Answer 16

f'

Answer 17

and its a good thing that they define f(4) and also f'(4) for us doesnt it

Answer 18

so =1/2(x)^-1/2 . f(4) + (x)^1/2 . f'(4) ?

Answer 19

close .. when x=4, then you might want to evaluate it all for x=4

Answer 20

g' (x)=1/2(x)^-1/2 . f(x) + (x)^1/2 . f'(x)

g' (4)=1/2(4)^-1/2 . f(4) + (4)^1/2 . f'(4)

Answer 21

like that ? =1/2(4)^-1/2 . f(4) + (4)^1/2 . f'(4) ?

Answer 22

exactly

Answer 23

thanks a lot :)

Answer 24

yep ;)