## Chain Rule - Do not understand step by step

Limits, differentiation, related rates, integration, trig integrals, etc.
Hans27
Posts: 3
Joined: Thu Jul 14, 2016 11:40 am
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### Chain Rule - Do not understand step by step

Hello people,

forgive me for my dumb questions,
but I am asking this question, which might seem stupid for some, in order to avoid paying almost 66 euros for a Wolfram Alpha Pro account (and risking not understanding it anyways)

x(t) = A*cosine(wt+Phi)

The first derivative is:

dx/dt = -Aw*sin(wt+Phi)

I know that this result is right, for the first derivative,
i just dont know how to get there, (step by step)

Both wolfram alpha
http://www.wolframalpha.com/input/?i=di ... ation+to+t

and Symbo lab

https://www.symbolab.com/solver/derivat ... )%5Cright)

give me the same results,

but Matlab doesn't explain it step by step

Symbolab in other hand explains kind of

but i still didnt understand why

I know what is the chain rule,

and i know that i should differentiate what is in side the parenthesis (wt+Phi) (which by the way is = w)

and I also understand that d/du cos(u) = -sin(u)

-A*sin(wt+Phi)*w

but i sincerely cannot get so far, the reason of thiw last "w"

in my limited comprehension the result should be = -A*sin(wt+Phi)

can anyone save me?

Thanks

Hans

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
Contact:

### Re: Chain Rule - Do not understand step by step

x(t) = A*cosine(wt+Phi)

The first derivative is:

dx/dt = -Aw*sin(wt+Phi)

I know that this result is right, for the first derivative,
i just dont know how to get there, (step by step)....
Use the Chain Rule. You have the constant "A" multiplied on a cosine; you carry the A along for the ride.

Look at the cosine. What's the derivative of cosine? Write that down, including whatever is inside the cosine. You multiply this by the "A" that was there in the first place.

Now, by the Chain Rule, look at whatever was inside the cosine; that's the wt + Phi. The w and the Phi are constants, so "wt + Phi" is similar to "3x + 4" when it comes to taking the derivative. What's the derivative of wt + Phi, with respect to "t"? You multiply this by whatever all you'd already had, from the previous steps.

Now that you've gotten down to "just the variable" (being the "t" in what you differentiated last), you've gone as far as you can go, and the Chain Rule is done.

So you had the "A" that you carried along, times the derivative of the cosine, times the derivative of the inside of the cosine. What did you get for this?