What is the derivative of secxtanx?

d/dx(uv)=u*dv/dx+v*du/dx

d/dx(secxtanx)=secx*[d/dx(tanx)]+tanx*[d/dx(secx)]

-The derivative of tanx is:

d/dx(tan u)=[sec(u)]2*d/dx(u)

d/dx(tan x)=[sec(x)]2*d/dx(x)

d/dx(tan x)=[sec(x)]2*(1)

d/dx(tan x)=(sec(x))2=sec2(x)

-The derivative of secx is:

d/dx(sec u)=[sec(u)tan(u)]*d/dx(u)

d/dx(sec x)=[sec(x)tan(x)]*d/dx(x)

d/dx(sec x)=[sec(x)tan(x)]*(1)

d/dx(sec x)=sec(x)tan(x)

d/dx(secxtanx)=secx*[sec2(x)]+tanx*[sec(x)tan(x)]

d/dx(secxtanx)=sec3(x)+sec(x)tan2(x)