find derivative 1/root(3-x)
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Answer:
Let
f
(
x
)
=
1
√
x
, then
y
=
1
u
and
u
=
x
1
2
, since
√
x
=
x
1
2
.
Simplifying further, we have that
y
=
u
and
u
=
x
−
1
2
The chain rule states
d
y
d
x
=
d
y
d
u
×
d
u
d
x
This means we have to differentiate both functions and multiply them. Let's start with
y
.
By the power rule
y
'
=
1
×
u
0
=
1
.
Now for
u
:
Once again by the power rule we get:
u
'
=
−
1
2
×
x
−
1
2
−
1
u
'
=
−
1
2
x
−
3
2
u
'
=
−
1
2
√
x
3
f
'
(
x
)
=
y
'
×
u
'
f
'
(
x
)
=
1
×
−
1
2
√
x
3
f
'
(
x
)
=
−
1
2
√
x
3
Hopefully this helps!
Step-by-step explanation:
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