Suppose F(x) = f(g(x)) and g(3) = 6, g '(3) = 4, f '(3) = 2, and f '(6) = 7. Find F '(3).

Question

amistre64 · Answer

chain rule ....

yb1996 · Answer

yes, I understand that I have to do chain rule, I just don't understand how I'm supposed to get the answer.

amistre64 · Answer

define the chain rule for me

yb1996 · Answer

the chain rule is f(gx))' = f'(gx)) g'(x)

amistre64 · Answer

correct

so lets just sub in the values they give you

f'(g(3)) * g'(3)

yb1996 · Answer

ok, so that would be f'(6) * 4 = 7 * 4 = 28
is that right?

amistre64 · Answer

yep

yb1996 · Answer

Ok, thank you. I also have another question. With chain rule how would I take the derivative of function like so: W = uov   ???

yb1996 · Answer

so, how would I find the derivative of W?

amistre64 · Answer

same way:  just the names have changed

uov = u(v)

derive: u'(v) * v'

amistre64 · Answer

im assuming u o v is the usual notation for function composition

yb1996 · Answer

so "o" implies multiplication?

amistre64 · Answer

not conventionally no.  'o' is shorthand for 'composed of'

fog means f, composed of g ... or simply f(g)

amistre64 · Answer

f*g means multiplication, or even fg

yb1996 · Answer

oh wait, uov means " u of v", is that right?

amistre64 · Answer

correct

yb1996 · Answer

ahhh, that makes things so much more clear. Thank you for the help!

amistre64 · Answer

youre welcome