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Math Help - Basic Differentiation help needed...

  1. #1
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    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.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by evans007 View Post
    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
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  3. #3
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    Thanks for that CB. So what would be your steps to answer it? cheers
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by evans007 View Post
    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
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