If `u = e^(ax) sin bx and v = e^(ax)cos bx`, then what is

Options

A. `a e^(2ax)`
B. `(a^(2)+b^(2)) e^(ax)`
C. ` ab e ^(2ax)`
D. `(a +b) e^(ax)`

Answer

A

Explanation

`u (du)/(dx) + v(dv)/(dx) = e^(ax)sin bx [ ae^(ax) sin bx+ be^(ax) cos bx]`
` = e^(ax) cos bx [ae^(ax) cos bx -be^(ax) sin bx] `
` e^(2ax) [a sin ^(2) bx +b sin bx cos bx+ a cos^(2) bx -b sin bx cos bx]`
` ae^(2ax)`