3 sin x-4 cot x+1 find dxdy
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Calculus Examples
Popular Problems Calculus Find the Derivative - d/dx y=3sin(x)cot(x)
y
=
3
sin
(
x
)
cot
(
x
)
Since
3
is constant with respect to
x
, the derivative of
3
sin
(
x
)
cot
(
x
)
with respect to
x
is
3
d
d
x
[
sin
(
x
)
cot
(
x
)
]
.
3
d
d
x
[
sin
(
x
)
cot
(
x
)
]
Differentiate using the Product Rule which states that
d
d
x
[
f
(
x
)
g
(
x
)
]
is
f
(
x
)
d
d
x
[
g
(
x
)
]
+
g
(
x
)
d
d
x
[
f
(
x
)
]
where
f
(
x
)
=
sin
(
x
)
and
g
(
x
)
=
cot
(
x
)
.
3
(
sin
(
x
)
d
d
x
[
cot
(
x
)
]
+
cot
(
x
)
d
d
x
[
sin
(
x
)
]
)
The derivative of
cot
(
x
)
with respect to
x
is
−
csc
2
(
x
)
.
3
(
sin
(
x
)
(
−
csc
2
(
x
)
)
+
cot
(
x
)
d
d
x
[
sin
(
x
)
]
)
Simplify the expression.
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3
(
−
sin
(
x
)
csc
2
(
x
)
+
cot
(
x
)
d
d
x
[
sin
(
x
)
]
)
The derivative of
sin
(
x
)
with respect to
x
is
cos
(
x
)
.
3
(
−
sin
(
x
)
csc
2
(
x
)
+
cot
(
x
)
cos
(
x
)
)
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