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Calculus Examples
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Calculus
Find the Derivative - d/dx sin(x)+cos(x)
sin
(
x
)
+
cos
(
x
)
sin
(
x
)
+
cos
(
x
)
Step 1
By the
Sum
Rule, the
derivative
of
sin
(
x
)
+
cos
(
x
)
sin
(
x
)
+
cos
(
x
)
with respect to
x
x
is
d
d
x
[
sin
(
x
)
]
+
d
d
x
[
cos
(
x
)
]
d
d
x
[
sin
(
x
)
]
+
d
d
x
[
cos
(
x
)
]
.
d
d
x
[
sin
(
x
)
]
+
d
d
x
[
cos
(
x
)
]
d
d
x
[
sin
(
x
)
]
+
d
d
x
[
cos
(
x
)
]
Step 2
The
derivative
of
sin
(
x
)
sin
(
x
)
with respect to
x
x
is
cos
(
x
)
cos
(
x
)
.
cos
(
x
)
+
d
d
x
[
cos
(
x
)
]
cos
(
x
)
+
d
d
x
[
cos
(
x
)
]
Step 3
The
derivative
of
cos
(
x
)
cos
(
x
)
with respect to
x
x
is
−
sin
(
x
)
-
sin
(
x
)
.
cos
(
x
)
−
sin
(
x
)
cos
(
x
)
-
sin
(
x
)
s
i
n
x
+
c
o
s
x
s
i
n
x
+
c
o
s
x
(
(
)
)
|
|
[
[
]
]
√
√
≥
≥
∫
∫
7
7
8
8
9
9
≤
≤
°
°
θ
θ
4
4
5
5
6
6
/
/
^
^
×
×
>
>
π
π
1
1
2
2
3
3
-
-
+
+
÷
÷
<
<
∞
∞
!
!
,
,
0
0
.
.
%
%
=
=
⎡
⎢
⎣
x
2
1
2
√
π
∫
x
d
x
⎤
⎥
⎦
[
x
2
1
2
π
∫
x
d
x
]
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