Find the derivative of the following functions:2tanx−7secx

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Filo · Accepted Answer

Let f(x)=2tanx−7secx Thus using first principle,f′=h→0lim​hf(x+h)−f(x)​= h→0lim​h1​[2tan(x+h)−7sec(x+h)−2tanx+7secx]= h→0lim​h1​[2{tan(x+h)−tanx}−7{sec(x+h)−secx}]= 2h→0lim​h1​[tan(x+h)−tanx]−7h→0lim​h1​[sec(x+h)−secx]= 2h→0lim​h1​[cos(x+h)sin(x+h)​−cosxsinx​]−7h→0lim​h1​[cos(x+h)1​−cosx1​]= 2h→0lim​h1​[cosxcos(x+h)sin(x+h)cosx−sinxcos(x+h)​]−7h→0lim​h1​[cosxcos(x+h)cosx−cos(x+h)​]= 2h→0lim​h1​[cosxcos(x+h)sin(x+h−x)​]−7h→0lim​h1​[cosxcos(x+h)−2(2x+x+h​)sin(2x−x−h​)​]= 2h→0lim​[(hsinh​)cosxcos(x+h)1​]−7h→0lim​h1​[cosxcos(x+h)−2sin(22x+h​)sin(−2h​)​]= 2(h→0lim​hsinh​)(h→0lim​cosxcos(x+h)1​)−7(2h​→0lim​2h​sin2h​​)(h→0lim​cosxcos(x+h)sin(22x+h​)​)= 2.1. cosxcosx1​−7⋅1(cosxcosxsinx​)= 2sec2x−7secxtanx

Question Text	Find the derivative of the following functions: $2 tan x - 7 sec x$
Answer Type	Text solution:1
Upvotes	150

Find the derivative of the following functions: $2 tan x - 7 sec x$

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