If f(x) = (logcot x tanx) (logtan x cot x)-1 + tan-1 (4x / 4 - x2 ), then f`(2) - Maths - Continuity and Differentiability

Question

If f(x) = (logcot x tanx) (logtan x cot
x)-1 + tan-1 (4x / 4 - x2 ), then
f`(2) is equal to????

Prasanta · Accepted Answer

f(x)=logcotxtanxlogtanxcotx-1 + tan-14x4-x2⇒f(x)=
logtanxlogcotx logcotxlogtanx + tan-12x21-x22

⇒f(x)=logtanxlogcotx2 + 2tan-1x2

∴f '(x)=2logtanxlogcotx1logcotx 1tanx sec2x +
logtanx-1log(cotx)21cotx-cosec2x + 211+x22 12 ⇒f
'(x)=2logtanxlogcotxsec2xtanx logcotx + logtanx cosec2xcotx
log(cotx)2 + 44+x2

So, f '(2)=2logtan2logcot2sec22tan2 logcot2 + logtan2 cosec22cot2
log(cot2)2 + 44+22 =2logtan2logcot2sec22tan2 logcot2 + logtan2
cosec22cot2 log(cot2)2 +12

If f(x) = (logcot x tanx) (logtan x cot x)-1 + tan-1 (4x / 4 - x2 ), then f`(2) is equal to????

If f(x) = (log_{cot x}tanx) (log_{tan x} cot x)^-1 + tan^-1 (4x / 4 - x² ), then f`(2) is equal to????