e^x²/1+x² find the differentiation
Answers
Answered by
0
Step-by-step explanation:
d
d
x
e
(
x
2
−
1
)
2
=
4
e
(
x
2
−
1
)
2
⋅
x
(
x
2
−
1
)
Explanation:
y
=
e
(
x
2
−
1
)
2
Let
u
=
(
x
2
−
1
)
2
such that
y
=
e
u
Now
d
y
d
x
=
d
y
d
u
⋅
d
u
d
x
To get the derivative of
u
, we use the chain rule again:
Let
v
=
x
2
−
1
such that
u
=
v
2
d
v
d
x
=
2
x
d
u
d
v
=
2
v
d
u
d
x
=
d
v
d
x
⋅
d
u
d
v
=
4
x
v
=
4
x
(
x
2
−
1
)
d
y
d
u
=
e
u
=
e
(
x
2
−
1
)
2
Now we can go back to the original equation:
d
y
d
x
=
d
y
d
u
⋅
d
u
d
x
=
e
(
x
2
−
1
)
2
⋅
4
x
(
x
2
−
1
)
In the answers, variables
v
and
u
were defined for the use of chain rule.
Answered by
0
By using chain rule we can solve this problem
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