Question

Derivative of sin x^0 with respect to X is??

Answer 1

Answer:

x^0 =1

and its d.w.r. to x is 0

Answer 2

Here is your answer

Use logarithmic differentiation.
y
=
(
sin
x
)
x
ln
y
=
ln
(
(
sin
x
)
x
)
=
x
ln
(
sin
x
)
(Use properties of
ln
)
Differentiate implicitely: (Use the product rule and the chain ruel)
1
y
d
y
d
x
=
1
ln
(
sin
x
)
+
x
[
1
sin
x
cos
x
]
So, we have:
1
y
d
y
d
x
=
ln
(
sin
x
)
+
x
cot
x
Solve for
d
y
d
x
by multiplying by
y
=
(
sin
x
)
x
,
d
y
d
x
=
(
ln
(
sin
x
)
+
x
cot
x
)
(
sin
x
)
x