# Thread: Basic Differentiation help needed...

1. ## 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.

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

CB

3. Thanks for that CB. So what would be your steps to answer it? cheers

4. Originally Posted by evans007
Thanks for that CB. So what would be your steps to answer it? cheers
$\displaystyle y = 3\sin(2t) + 4\cos(2t)$

so:

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

then you use the chain rule to get:

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

and:

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

from that you should be able to finish this yourself.

CB