I am having a conflict with two different ways of finding a derivative.(adsbygoogle = window.adsbygoogle || []).push({});

Here is the function:

y=10*sinpi(.01x-2.00t)

Yes, that pi is after sin, but not in the paranthesis. This is how the prof gave it to us. This may be my problem, how I am treating the pi. I figure it was factored out of the parenthesis. So, to find the partial derivative WRT t by hand I do this:

y=10*sin(.01pi*x - 2.00pi*t) I multiplied the pi into the ()

dy/dt = -2.00pi*10*cos(.01pi*x - 2.00pi*t) used the chain rule

dy/dt = -20pi*cos(.01pi*x - 2.00pi*t) final result

That is my result. I check this in Matlab by entering the following:

>> syms x t

>> diff(10*sin(pi*.01*x-pi*2*t),t)

ans =

-20*cos(1/100*pi*x-2*pi*t)*pi

So with that I am happy. Now the tricky question.

If I enter this same thing to my TI-89, I get:

-62.8319*cos(2pi*t - .031416*x)

Now...it just hit me that you can transpose the items inside the paranthesis of cosine, and it is the same result. Ok, duh. I don't want to delete everything I just typed. My next question...

Am I treating the pi correctly to begin with? Is it correct to multiply it into the () like that? If not, what should I do with it? Is there an easier way?

Thanks.

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# Weird derivative conflict

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