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

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Answer 1 · 2016-03-03T23:44:29

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)#