Differentiate cos x w.r.t x using first principle
Answers
Answered by
3
Answer:
-sinx
Step-by-step explanation:
f
′
(x)=
h→0
lim
h
f(x+h)−f(x)
=
h→0
lim
h
cos(x+h)−cosx
=
h→0
lim
[
h
cosxcosh−sinxsinh−cosx
]
=
h→0
lim
[
h
−cosx(1−cosh)−sinxsinh
]
=
h→0
lim
[
h
−cosx(1−cosh)
=
h
sinxsinh
]
=−cosx(
h→0
lim
h
1−cosh
)−sinx
h→0
lim
(
h
sinh
)
=−cosx.(0)−sinx(1)=−sinx
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