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 May 12th, 2017, 03:37 AM #1 Newbie   Joined: May 2017 From: alabama Posts: 6 Thanks: 0 differentiation Can anybody tell me where I've gone wrong on this question? An alternating current, i amperes, is given by i = 15 cos (2pi f t) Calculate the rate of change of current when t = 2 ms and f = 75 Hz. dy/dx = dy/du × du/dx y = 15 cos du/dt = -15sin = (15) (2pi f) - sin 2 pi f t = (15) (2 pi × 75) - sin (2pi × 75 × 2×10-3) = 7067.77 a/s Last edited by skipjack; May 12th, 2017 at 05:53 AM.
May 12th, 2017, 03:56 AM   #2
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Quote:
 Originally Posted by tommyturner1993 Can anybody tell me where I've gone wrong on this question? An alternating current, i amperes, is given by i = 15 cos (2pi f t) Calculate the rate of change of current when t = 2 ms and f = 75 Hz. dy/dx = dy/du × du/dx y = 15 cos du/dt = -15sin = (15) (2pi f) - sin 2 pi f t = (15) (2 pi × 75) - sin (2pi × 75 × 2×10-3) = 7067.77 a/s
You mean, I think, that u= 2pi ft and y= 15 cos(u). Then dy/du= -15 sin(u) and du/dt= 2pi f. The chain rule gives dy/dt= (2pi f)(-15 sin(2pi ft)= -30pi f sin(2pi ft). You appear to have added the two derivatives rather than multiplying.

Quote:
 =(15) (2 pi × 75) - sin (2pi × 75 × 2×10-3) =7067.77 a/s
With t = 2 ms and f = 75 Hz we have dy/dt= -30pi (75) sin(2pi (75)(2))= (7068 )(sin(942))= (7068 )(-0.459)=-3250.

Last edited by skipjack; May 12th, 2017 at 05:52 AM.

 May 12th, 2017, 04:56 AM #3 Math Team   Joined: Jul 2011 From: Texas Posts: 2,751 Thanks: 1401 Assuming frequency is constant since no information is given if or how it changes w/respect to time ... $i=15\cos(150\pi t)$ $\dfrac{di}{dt} = -2250\pi \sin(150\pi t)$ At $t=0.002 \, sec$ ... $\dfrac{di}{dt}=-2250\pi \sin\left(\dfrac{3\pi}{10}\right) \approx -5718.6 \, amps/sec$ Thanks from phrack999
 May 12th, 2017, 05:10 AM #4 Newbie   Joined: May 2017 From: alabama Posts: 6 Thanks: 0 Well I redid the question and I have the same answer as you skeeter. Do you know where country boy got the answer -3250 from? Last edited by skipjack; May 12th, 2017 at 05:54 AM.
 May 12th, 2017, 05:58 AM #5 Global Moderator   Joined: Dec 2006 Posts: 18,956 Thanks: 1603 He didn't convert 2 ms to seconds.

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