Find derivative of x sec x by first principle
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Answer:
Let f(x)=secx
f(x+h)=sec(x+h)
f
1
(x)=
h→0
lim
h
f(x+h)−f(x)
=
h→0
lim
h
sec(x+h)−secx
=
h→0
lim
h
cos(s+h)
1
−
cosx
1
=
h→0
lim
cos(x+h)cosxh
cosx−cos(x+h)
=
h→0
lim
cos(x+h)cosxh
−2sin[
2
2x+h
]sin[
2
−h
]
=
h→0
lim
cos(x+h)cosxh
2sin[
2
2x+h
]sin
2
h
[sin(−θ=−sinθ)]
=
h→0
lim
2
2
h
2sin
2
h
×
h→0
lim
cos(x+h)cosx
h→0
lim
sin
2
(2x+h)
=1×
cos(x+0)cosx
sin(
2
2x+0
)
=
cosxcosx
sinx
=tanxsecx
Step-by-step explanation:
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