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Byju's Answer
Standard XII
Mathematics
Differentiation to Solve Modified Sum of Binomial Coefficients
If y=x+ex, th...
Question
If y = x + e
x
, then
d
2
x
d
y
2
= ______________.
Open in App
Solution
y
=
x
+
e
x
Differentiating both sides with respect to x, we get
d
y
d
x
=
d
d
x
x
+
e
x
⇒
d
y
d
x
=
1
+
e
x
⇒
d
x
d
y
=
1
1
+
e
x
d
x
d
y
=
1
d
y
d
x
Differentiating both sides with respect to y, we get
d
d
y
d
x
d
y
=
d
d
y
1
1
+
e
x
⇒
d
2
x
d
y
2
=
0
-
1
×
d
d
y
1
+
e
x
1
+
e
x
2
⇒
d
2
x
d
y
2
=
-
0
+
e
x
d
x
d
y
1
+
e
x
2
⇒
d
2
x
d
y
2
=
-
e
x
1
1
+
e
x
1
+
e
x
2
d
x
d
y
=
1
1
+
e
x
⇒
d
2
x
d
y
2
=
-
e
x
1
+
e
x
3
If y = x + e
x
, then
d
2
x
d
y
2
=
-
e
x
1
+
e
x
3
.
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2
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Differentiation to Solve Modified Sum of Binomial Coefficients
Standard XII Mathematics
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