Question Number 102508 by Study last updated on 09/Jul/20

lim_(△x→0) ((e^(sin(x−△x)) −e^(sinx) )/(△x))=?

Commented bybemath last updated on 09/Jul/20

may be lim_(Δx→0) ((e^(sin (x+Δx)) −e^(sin x) )/(Δx))

Commented byStudy last updated on 09/Jul/20

no sir

Commented byStudy last updated on 09/Jul/20

help me

Commented bybemath last updated on 09/Jul/20

using LHopital

Commented byDwaipayan Shikari last updated on 09/Jul/20

llim_(x→0) ((e^(sinx) (e^(sin(x−△x)−sinx) ))/(△x))=((e^(sinx) (e^(−2cos(x−((△x)/2))sin((△x)/2)) ))/(△x))=e^(sinx) .(e^(−cosx△x) /(△x)) e^(sinx−cosx△x) .(1/(△x))=y If( e^(sin(x+△x)) −e^(sinx) ).(1/(△x))=cosx e^(sinx)