Question #38190

1 Answer
Feb 13, 2018

The answer is tanx+xsec^2xtanx+xsec2x

Explanation:

Using the product rule for differentiation ,
dy/dx=xtanxdydx=xtanx
Let x=u and v=tanx

By product rule ,
dy/dx= v.du/dx + u.dv/dxdydx=v.dudx+u.dvdx ------(i)

Now , du/dx=1dudx=1 and dv/dx=sec^2xdvdx=sec2x

Substituting these into (i) you get ,
dy/dx=tanx+xsec^2xdydx=tanx+xsec2x

:. The answer is tanx + xsec^2x