dy/dx (2cos²x)² - cosec X .
Answers
Answered by
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Step-by-step explanation:
We want find the derivative of
y
=
cot
(
x
)
=
cos
(
x
)
sin
(
x
)
Use the quotient rule, if
y
=
f
g
then
d
y
d
x
=
f
'
⋅
g
−
f
⋅
g
'
g
2
, thus
f
=
cos
(
x
)
⇒
f
'
=
−
sin
(
x
)
g
=
sin
(
x
)
⇒
g
'
=
cos
(
x
)
Thus
d
y
d
x
=
−
sin
(
x
)
⋅
sin
(
x
)
−
cos
(
x
)
cos
(
x
)
sin
2
(
x
)
=
−
(
sin
2
(
x
)
+
cos
2
(
x
)
)
sin
2
(
x
)
=
−
1
sin
2
(
x
)
=
−
csc
2
(
x
)
Or
d
d
x
cot
(
x
)
=
−
csc
2
(
x
)
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