Question

How do you differentiate `f(x) =[(sin x + tan x)/(sinx* cos x)]^3`?

Answer 1

Rewrite this as

#f(x) =[(sin x + tan x)/(sinx* cos x)]^3=> f(x)=[(sinx+sinx/cosx)/(sinx*cosx)]=> f(x)=[(1+cosx)/cos^2x]^3#

Hence its derivative is

`(df)/dx=3*[(1+cosx)/cos^2x]^2*(d[(1+cosx)/cos^2x])/dx`

Now we have that

`d/dx((1+cos(x))/(cos^2(x))) = (cos(x)+2)*tan(x)*sec^2(x)`

Finally

`(df)/dx=3*[(1+cosx)/cos^2x]^2*(cos(x)+2)*tan(x)*sec^2(x)`