Calculus question- differentiation

[tracey163]

Could someone please help me with the method and steps to this question:

Find dy/dx for the following:

y = (5e^(2+ix))/(3e^(1-2ix))

 

[koushdcurryman]

Simplify it so it is of the form constant*e^(something) and then carry out differentiation of exponentials as you would.

 

[tracey163]

This is the way I tried to do it:

(Quotient rule)
dy/dx = ((5ie^(2 + ix))(3e^(1-2x)) - (-6ie^(1 - 2ix))(5e^(2 + ix))) / ((3e^(1 - 2ix))^2)

= (15ie^(3 - ix) + 30ie^(3 - ix)) / (9(e^(1 - 2ix))^2)

= (45ie^(3 - ix)) / (9(e^91 - 2ix)^2)

= (5ie^(3 - ix)) / ((e^(1 - 2ix))^2)

And I'm not sure where to go from there its either wrong or it needs simplifying some more...

 

[tracey163]

Ah thanks, yeah your right, I've got it :) it all makes perfect sense now :)

y = 5/3.e^(2 + ix - (1 - 2ix))

=5/3.e^(1 + 3ix)

dy/dx = 5ie^(1 + 3ix)

:D thanks!

 

[koushdcurryman]

You're welcome :-)