Question

Find the n^th derivative of y=e^ax cos2 x sin x.

Answer 1

Given `y = e^(ax) cos^2xsin x`

`y = e^(ax)((1+cos2x)/2)sinx`

`y=1/2(e^(ax)sinx+e^(ax)cos2xsinx)`

`y =1/2(e^(ax)sinx+1/2e^(ax)(sin3x-sinx))`

`y=1/2(1/2e^(ax)sin3x+1/2e^(ax)sinx)`

Diff n times,

`y_n=1/2(1/2 e^(ax)(sqrt(a^2+9))^nsin(3x+ntan^(-1)  3/a)+1/2e^(ax)(sqrt(a^2+1))^n sin(x+n tan^(-1) 1/a)).`