find the derivative of √ x with respect to x
Answers
Answered by
2
Answer:
Definition
f
'
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
By Definition,
f
'
(
x
)
=
lim
h
→
0
√
x
+
h
−
√
x
h
by multiplying the numerator and the denominator by
√
x
+
h
+
√
x
,
=
lim
h
→
0
√
x
+
h
−
√
x
h
⋅
√
x
+
h
+
√
x
√
x
+
h
+
√
x
=
lim
h
→
0
x
+
h
−
x
h
(
√
x
+
h
+
√
x
)
by cancelling out
x
's and
h
's,
=
lim
h
→
0
1
√
x
+
h
+
√
x
=
1
√
x
+
0
+
√
x
=
1
2
√
x
Hence,
f
'
(
x
)
=
1
2
√
x
.
I hope that this was helpful.
Answered by
0
Answer:
Step-by-step Convert the square root to its exponential form and then use the power rule.
y
=
√
x
=
x
1
2
Now bring the power of
1
2
down as a coefficient and then subtract 1 from the current power of
1
2
. Evaluate the fractions and simplify. Manipulate exponents from negative to positive.
y
'
=
1
2
x
(
1
2
−
1
)
=
1
2
x
(
1
2
−
2
2
)
=
1
2
x
(
−
1
2
)
=
1
2
x
1
2
=
1
2
√
x
:
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