=0 ⇒f(x) is differentiable at x=0 Differentiability of h(x) at x=0 h'(0+)=1,h(x) is an even function hence non diff at x=0 Differentiability of f(h(x) at x=0 f(h(x))=g(e|x|)∀x∊ℝ LHD f′(h(0−))=
lim
δ→0
f(h(0))−f(h(0−δ))
δ
=
lim
δ→0
g(1)−g(eδ)
δ
=−g′(1) RHD f′(h(0+))=
lim
δ→0
f(h(0−δ))−f(h(0))
δ
=
lim
δ→0
g(eδ)−g(1)
δ
=−g′(1) Since g'(1)≠0⇒f(h(x)) is no diff at x=0 Differentiability of h(f(x)) at x=0 h(f(x))={