My Math Forum Derivative of Trig and Euler's number

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March 1st, 2017, 01:43 PM   #1
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Derivative of Trig and Euler's number

I have a problem I am having touble solving (refer to image question 1 b).

I cannot find any tutorial explaining how to solve Trig and e^x derivatives together.

I'm a little rusty with my math, so if anyone could please provide a step by step solution that would be great.

I understand the derivative of e^x = e^x & cosx is -sinx.

But I'm not sure how to get the solution:

-(e^-4t)(80 cos 50t + 1000 sin 50t) μC

Thanks.
Attached Images
 Q1b.jpg (8.2 KB, 8 views)

Last edited by skipjack; March 1st, 2017 at 03:10 PM.

 March 1st, 2017, 02:15 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra The product rule for differentiation says $$\frac{\mathrm d}{\mathrm dx}(uv) = v\frac{\mathrm du}{\mathrm dx} + u\frac{\mathrm dv}{\mathrm dx}$$ for functions $u(x)$ and $v(x)$.
 March 1st, 2017, 02:39 PM #3 Member   Joined: Jan 2014 Posts: 42 Thanks: 0 Thank you Ahh yes, that's right. I will try and solve now. Thanks. Last edited by skipjack; March 1st, 2017 at 03:10 PM.
March 1st, 2017, 03:42 PM   #4
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Ok I am missing something here, I am getting an inverse answer:

hope you can make sense of my answer haha.
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 March 1st, 2017, 04:07 PM #5 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 I don't know what you man by "inverse answer". What you give, $q'(t)= e^{-4t}(-80 cos(50t)- 1000 sin(50t))$, is the correct answer.
 March 1st, 2017, 05:01 PM #6 Member   Joined: Jan 2014 Posts: 42 Thanks: 0 sorry I didn't not see the '-' symbol in front of the answer I posted in my first post. Thanks for your help

 Tags derivative, derivitive, euler, eulers, number, trig

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