What Is The Nth Derivative Of E^(-3) * Cos^(3)X ?

[StarDiwakar]

Can someone please help me with this problem?
I know that we cannot use Leibnitz theorem but what are the steps to be used in solving this?

[Obiter]

If The Hitchhikers Guide to the Galaxy is to be believed then the answer is 42.

[factor-fiction]

Is the question right?

Is the function definitely e¯³ * cos³ x ?

[grasscarp]

Answered here
http://www.mathskey.com/question2answer/7064/find-the-nth-derivative-of-e-3-x-sin-2-x-cos-3-x

[factor-fiction]

Let y= e¯³ * cos³ x

Then
dy/dx =e¯³ * d(cos³ x)/dx

Work that out.
Then repeat.
Then repeat again.
Followthe pattern to find the nth deriivative

[factor-fiction]

I think the first derivative works out as

3e¯³ * cos² x

Then continue

[factor-fiction]

Grasscarp's link is for a similar problem.
Have a go- it's the best way to become competent at these.
Post your solution or partial soloution here and we'll comment/help.
Jim360 is the main man on these

[factor-fiction]

Oops , looking back at this I missed out part of answer for the derivative of the cos³ x bit, but I'm sure you can work it out. It's not easy doing this without pen and paper but think the last line should have said:

dy/dx= -3e¯³ * (cos²x)(sinx)


There may be a clever rule you can use to solve these but if you don't know one just do it step by step, continually differentiating (using chain rule and product rule) and see if a pattern emerges.

[factor-fiction]

Awww- "user is inactive". I hope it wasn't something I said