differentiate the following with respect to x :√(x^2 +x+1)
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How do you find the derivative of
y
=
x
√
x
2
+
1
?
Calculus Chain Rule
1 Answer
Gaurav
Sep 4, 2014
y
'
=
1
(
x
2
+
1
)
3
2
Solution :
y
=
x
√
x
2
+
1
Using Quotient Rule, which is
y
=
f
g
, then
y
'
=
g
f
'
−
f
g
'
g
2
similarly following for the given problem, yields
y
'
=
√
x
2
+
1
−
x
⋅
1
2
√
x
2
+
1
⋅
(
2
x
)
(
√
x
2
+
1
)
2
y
'
=
√
x
2
+
1
−
x
2
√
x
2
+
1
x
2
+
1
y
'
=
(
x
2
+
1
)
−
x
2
(
x
2
+
1
)
3
2
y
'
=
1
(
x
2
+
1
)
3
2
Answer link
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Chain Rule
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