How do you find the derivative of ##secx tanx##?

Use the and derivatives of trigonometric functions.

##d/dx(secx tanx) = d/dx(secx) tanx + secx d/dx(tanx)##

## = (secxtanx)tanx+secx(sec^2x)##

## = sec tan^2x + sec^3x##

## = secx(tan^2x+sec^2x)##