# How do you find the derivative of Inverse trig function #y = tan(x + sec x)#?

##### 1 Answer

Aug 26, 2015

#### Explanation:

All you really need to use in order to differentiate this function is the chain rule for

#color(blue)(d/dx(tanx) = sec^2x)" "# and#" "color(blue)(d/dx(secx) = secx * tanx)#

So, the derivative of

#d/dx(y) = d/(du)(tanu) * d/dx(u)#

#y^' = sec^2u * d/dx(x + secx)#

#y^' = sec^2u * (1 + secxtanx)#

#y^' = color(green)(sec^2(x+secx) * (1 + secxtanx))#