Differentiation

Sully

Folks..

Can someone refresh my memory on how to apporach this;

f(t) = sin(2t) + 3
f'(t) = ?

I cant remember the rule for number inside the bracket. I thought it might be the chain rule but I cant seem to figrue that one out.

Any ideas?

gra26

you should have f(t)=sin(2t) +3

But anyways, It is the chain rule, you're right. What are you not sure about?

Sully

I seem to have forgotten the chain rule, and I knew it very well a few months ago. I looked at a few examples on the net but wasnt confident enough with it. Im very poor at Maths so any recommendations on how to approach this using the chain rule?

Michael Collins

You're dead right. It is the chain rule:

We let u = 2t, so now we have

f(u) = sin(u)

we want df(t)/dt, but by the chain rule we have

df(u)/dt = (df(u)/du) * (du/dt) = cos(u) * 2
df(t)/dt = cos(t) * 2 = 2cos(t)

of course after seeing the once you can just write out the answer without going through the formal chain rules process.

gra26

Let y= sin (2t) + 3
Look and see whats causing you the most hassle, as in if you didn't have *** then you could do the question no problem.

Let u= *** and then rewrite y in terms of u.

Then remember what you want is dy/dt (or f'(t)) and that
dy/dt = dy/du * du/dt

Sully

I assume to do the chain rule..

1) Establish the inner/outter function,
2) Find derivative of outter function,
3) Do above with inner function,
4) Multiply inner function by outer function.

I dont think you actually solve 4, do you?

gra26

Well having done (4) that would be the answer.

gra26

And I assume you mean multiply the derivative of the inner function by the derivative of the outer function? and not multiply the inner function by the outer function

Sully

gra26 wrote: »

And I assume you mean multiply the derivative of the inner function by the derivative of the outer function? and not multiply the inner function by the outer function

Yup

gra26

Yeah so if you check out what michael collins wrote, the u is the inner function and f(u) is the inner function

seandoiler

Michael Collins wrote: »

You're dead right. It is the chain rule:

We let u = 2t, so now we have

f(u) = sin(u)

we want df(t)/dt, but by the chain rule we have

df(u)/dt = (df(u)/du) * (du/dt) = cos(u) * 2
df(t)/dt = cos(t) * 2 = 2cos(t)

of course this answer should be 2 cos(2t) by the way...just pointing out like

Michael Collins

seandoiler wrote: »

of course this answer should be 2 cos(2t) by the way...just pointing out like

Yep, thanks.