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Byju's Answer
Standard XII
Mathematics
Inverse of a Function
If x=ex/y, ...
Question
If
x
=
e
x
y
, prove that
d
y
d
x
=
x
−
y
x
log
x
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Solution
Applying Log on both sides
l
o
g
x
=
x
y
l
o
g
e
y
l
o
g
x
=
x
Differentiating wrt x
l
o
g
x
d
y
d
x
+
y
x
=
1
l
o
g
x
d
y
d
x
=
x
−
y
x
d
y
d
x
=
x
−
y
x
l
o
g
x
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If
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