# Basic Differentiation help needed...

• Aug 3rd 2009, 06:10 AM
evans007
Basic Differentiation help needed...
Hi there, basically I am learning differentiation and have the task of finding "the gradient of y = 3sin2t + 4cos2t, when t=2" using radians. I don't neccessarily need the answer to this, I would like to know the procedure used when tackling a question like this.

Thank you for reading, any help or links to video tutorials would be great. I just need to know how to get to the answer, thank you.
• Aug 3rd 2009, 07:19 AM
CaptainBlack
Quote:

Originally Posted by evans007
Hi there, basically I am learning differentiation and have the task of finding "the gradient of y = 3sin2t + 4cos2t, when t=2" using radians. I don't neccessarily need the answer to this, I would like to know the procedure used when tackling a question like this.

Thank you for reading, any help or links to video tutorials would be great. I just need to know how to get to the answer, thank you.

Asking for the gradient at $t=2$ is effectivly asking for $\left. \frac{dy}{dt}\right|_{t=2}$ in this case.

CB
• Aug 3rd 2009, 07:30 AM
evans007
Thanks for that CB. So what would be your steps to answer it? cheers
• Aug 3rd 2009, 07:40 AM
CaptainBlack
Quote:

Originally Posted by evans007
Thanks for that CB. So what would be your steps to answer it? cheers

$y = 3\sin(2t) + 4\cos(2t)$

so:

$\frac{dy}{dt}=3 \frac{d}{dt}\sin(2t) + 4 \frac{d}{dt}\cos(2t)$

then you use the chain rule to get:

$\frac{d}{dt}\sin(2t)= 2\cos(2t)$

and:

$\frac{d}{dt}\cos(2t)=-2\sin(2t)$

from that you should be able to finish this yourself.

CB