differentiation of x^2-cosx+1/x
Answers
Answered by
1
Step-by-step explanation:
Recall that we use the quotient rule to differentiate a function of the form
P
(
x
)
Q
(
x
)
.
The quotient rule states that:
d
d
x
P
(
x
)
Q
(
x
)
=
Q
(
x
)
⋅
P
'
(
x
)
−
P
(
x
)
⋅
Q
'
(
x
)
(
Q
(
x
)
)
2
I usually remember it as
B
T
'
−
T
B
'
B
2
where
T
is the top function and
B
is the bottom function.
Now, applying the quotient rule to the function, we get:
d
d
x
2
cos
x
x
+
1
=
(
x
+
1
)
(
−
2
sin
x
)
−
(
2
cos
x
)
(
1
)
(
x
+
1
)
2
=
−
2
x
sin
(
x
)
−
2
sin
(
x
)
−
2
cos
(
x
)
x
2
+
2
x
+
1
or
=
(
−
2
)
(
x
sin
(
x
)
+
sin
(
x
)
+
cos
(
x
)
)
x
2
+
2
x
+
1
Answered by
1
Answer:
2 x + sin x - 1/x^2
Step-by-step explanation:
Differentiation of x^2 is 2x.
Differentiation of cos x is - sinx.
Differentiation of 1/x is -1/x^2.
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