Finding the nth derivative of e^ax*sin(ax+b)

[Tanny Nusrat]

i have solved the following one but not sure...anyone give me the solve..i want to be sure..

nth derivative of {e^ax * Sin(ax+b)}

 

[andrewkirk]

Show your solution and your working, as requested in the sub-forum guidelines, and I'm sure somebody will confirm it, or correct it if wrong.

You need to use the product rule. Once you've differentiated several times you'll see a cyclic pattern that can be written down as a set of four cases.

 

[Tanny Nusrat]

ok..here is my solution...somebody please confirm me..

b^n * e^ax * Sin {(n*pi/2)+(bx+c)} + n*a*b* e^ax * Sin {pi/2+(bx+c)} + a^n * e^ax * Sin (b+c)

 

[andrewkirk]

Substitute n=1 into your formula and then compare to what you get when you differentiate once, ie $\frac{d}{dx}\big(e^{ax}\sin(ax+b)\big)$.

Do they look the same?

Post the working by which you arrived at your conclusion and somebody can show where you went wrong. Did you try what I suggested in post 2?

If you use latex to properly display your formulas you will also improve your chances of getting help. The latex tutorial is here.

 

[HallsofIvy]

Your original function has "ax+ b" while your formula for the nth derivative has "bx+ c". Was one of those a misreading?