find the derivative of the function cot x from the first principle
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Answered by
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-cosec²x is the solution to your problem
Answered by
0
Answer:
Derivative of
cot
(
x
)
is equal to
−
csc
2
(
x
)
.
Explanation:
We know that
cot
(
x
)
=
1
tan
(
x
)
so
f
'
(
x
)
=
1
tan
(
x
)
d
x
We can use the quotient rule to solve for the derivative. The quotient rule states:
d
(
g
(
x
)
h
(
x
)
)
=
(
g
'
(
x
)
h
(
x
)
−
g
(
x
)
h
'
(
x
)
g
(
x
)
2
)
d
x
in our case,
g
(
x
)
=
1
h
(
x
)
=
tan
(
x
)
g
'
(
x
)
=
0
h
'
(
x
)
=
sec
2
(
x
)
Let's plug these values back into the quotient rule:
0
⋅
tan
(
x
)
−
1
⋅
sec
2
(
x
)
tan
2
(
x
)
=
−
sec
2
(
x
)
tan
2
(
x
)
=
−
csc
2
(
x
)
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