Answer:
Step-by-step explanation:
You could do the question the way it is written, but it is far easier to bring the negative power up to the numerator.
y= x^2 - 3. The derivative of that is
dy/dx = 2x The three is a constant and is always dropped when a derivative is taken
d(-3)/dx = 0
If you are a purist and want to solve the question the way it is written, you could do it this way.
dy/dx = d(1)/dx x^-2 - d(x^-2)/dx * 1
======================
(x^-2)^2
dy/dx = - (-2 x^ - 3) / x^-4
dy/dx = 2 x^-3 * x^4
dy/dx = 2 x^(-3 + 4)
dy/dx = 2x ^ 1
dy/dx = 2x <<<<< answer
1) is correct.
2) is correct.
3) is correct.
4) is correct.
5) is not there.
6) is your first choice.
7) is incorrect is your second choice.
8) is your first choice.
13) is your last choice.
14) is your last choice.
15) is your third choice.
-3 2/5 - 5/6 = -127/30
-2/3 + 6 1/8 = 107/24
Answer:1/2 y
Step-by-step explanation:
We can solve this using ration reasoning:
x
2
x
1
=
y
2
y
1
Explanation:
If
x
varies directly with
y
(written
x
∝
y
), then doubling
y
means doubling
x
, so the rations of final values and initial values will be the same:
x
2
x
1
=
y
2
y
1
In this case,
x
2
9
=
24
18
x
2
=
9
⋅
24
18
=
12
Or, intuitively, if
x
∝
y
and
x
=
9
when
y
=
18
, we can conclude that
x
=
1
2
y
and
1
2
of 24 is 12.
