f(x)=a^√x find f'(x)
plase use this method
f'(x)=Lim h tends to 0 f(x+h)-f(x)/h
Answers
Answered by
0
Step-by-step explanation:
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.
Similar questions