Differentiation w/ complex exponential: d^2017/dt^2017 [sinh(-t) sin(-sqrt(3)t)]

[lilym22]

Hi there,

Could someone please help with the following problem:



I understand how to approach the problem if there was an exponential function outside the front of the trig function, but this is a hyperbolic so im a bit confused

Thank you

 

[Dr.Peterson]

Hi there,

Could someone please help with the following problem:

View attachment 10076

I understand how to approach the problem if there was an exponential function outside the front of the trig function, but this is a hyperbolic so im a bit confused

Thank you

Please show how you would do this with an exponential function. Presumably you would find the first several derivatives, see a pattern, and extend it. Do the same here, of show us why it isn't working for you.

 

[pka]

Hi there,

Could someone please help with the following problem:

View attachment 10076

I understand how to approach the problem if there was an exponential function outside the front of the trig function, but this is a hyperbolic so im a bit confused

The object is for you to do many derivatives to identify a pattern related to the order of the derivative.
Here is the fourth derivative.
Here is the tenth derivative.

You can use Wolframalpha to see other orders.