The result of differentiating Y=2׳ is
Answers
Answered by
0
Answer:
We will differentiate implicitly. This means, that whenever we differentiate a variable that's not
x
, the chain rule will kick in. Take a look at a couple examples before starting here:
d
d
x
x
3
=
3
x
2
but
d
d
x
y
3
=
3
y
2
d
y
d
x
d
d
x
x
=
1
but
d
d
x
y
=
d
y
d
x
d
d
x
x
y
2
=
(
d
d
x
x
)
y
2
+
x
(
d
d
x
y
2
)
=
y
2
+
x
(
2
y
)
d
y
d
x
So, for the given example, we see that we will use the power rule on the left-hand side. On the right, don't be misled by the two-thirds power:
a
2
3
is still a constant.
d
d
x
(
x
2
3
+
y
2
3
)
=
d
d
x
a
2
3
Power rule:
2
3
x
−
1
3
+
2
3
y
−
1
3
d
y
d
x
=
0
Multiply both sides by
3
2
:
x
−
1
3
+
y
−
1
3
d
y
d
x
=
0
1
x
1
3
+
1
y
1
3
d
y
d
x
=
0
Solving for
d
y
d
x
:
1
y
1
3
d
y
d
x
=
−
1
x
1
3
d
y
d
x
=
−
y
1
3
x
1
3
=
−
(
y
x
)
1
3
=
−
3
√
y
x
Similar questions