# Math Help - Differentiation Help!

1. ## Differentiation Help!

Hi,

f(t) = t Cos w t
f '(t) =
f ''(t) =

Can someone help quick please and tell me how to get the the answers and what rule it is!
thanks

2. I think i have worked it out now!
Product rule?!
f '(t) = Coswt - wtsinwt
f ''(t) = ?!?!?!?!

I think i have worked it out now!
Product rule?!
f '(t) = Coswt - wtsinwt
f ''(t) = ?!?!?!?!
Hello,

1. you used product rule and chain rule - and your result is OK

2. Use chainrule on the first summand and product rule and chain rule on the second summand. I've got:

$f''(t) = -t \cdot w^2 \cdot \cos(w \cdot t)-2w \cdot \sin(w\cdot t)$

4. for f ' (t) i used the product rule !

Can u give me a step by step of f '' (t) please.... because im confused!

for f ' (t) i used the product rule !

Can u give me a step by step of f '' (t) please.... because im confused!
Hi,

Ok here we go:
Your result: $f '(t) = \cos(wt) - wt\sin(wt)$

$
f '(t) = \cos(wt) - wt\sin(wt)=-w(\underbrace{t \cdot \sin(wt)}_{\text{use product rule}}) + \underbrace{\cos(wt)}_{\text{use chain rule}}$

$f''(t)=-w(\sin(wt)+t \cdot (cos(wt) \cdot w)-\sin(wt) \cdot w$
Expand the bracket and collect like terms.