How to do this derivative

Question

f(thetha)=(thetha)(tanthetha)(secthetha)

 

Please guide me through steps

Answer 1

f(θ) = θtanθsecθ = (θsinθ)/cos²θ is a nice simplification; I intend to use the Quotient Rule. Let this be u/v

so that u' = sinθ + θcosθ  and  v' = -2cosθsinθ  (note that I've used the product rule to differentiate u and the chain rule during differentiation of v (w.r.t. θ)

 

f'(θ) = (u'v - uv')/v²  is the Quotient Rule; just substitute for u, v,  u' and v' and simplify as much as you like.