y = (√x / x+1) ^2 diffrenciate it
Answers
Answered by
1
Answer:
Rewrite y as
y
=
√
1
+
x
2
=
(
1
+
x
2
)
1
2
differentiate using the
chain rule
d
d
x
(
f
(
g
(
x
)
)
)
=
f
'
(
g
(
x
)
)
.
g
'
(
x
)
...
...
...
...
...
...
.
.
(
A
)
--------------------------------------------------------
f
(
g
(
x
)
)
=
(
1
+
x
2
)
1
2
⇒
f
'
(
g
(
x
)
)
=
1
2
(
1
+
x
2
)
−
1
2
g
(
x
)
=
1
+
x
2
⇒
g
'
(
x
)
=
2
x
------------------------------------------------------
Substitute these values in (A)
1
2
(
1
+
x
2
)
−
1
2
.2
x
=
x
(
1
+
x
2
)
−
1
2
⇒
d
y
d
x
=
x
(
1
+
x
2
)
1
2
=
x
√
1
+
x
2
Step-by-step explanation:
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