Answer:
1. y' = 3x² / 4y²
2. y'' = 3x/8y⁵[(4y³ – 3x³)]
Step-by-step explanation:
From the question given above, the following data were obtained:
3x³ – 4y³ = 4
y' =?
y'' =?
1. Determination of y'
To obtain y', we simply defferentiate the expression ones. This can be obtained as follow:
3x³ – 4y³ = 4
Differentiate
9x² – 12y²dy/dx = 0
Rearrange
12y²dy/dx = 9x²
Divide both side by 12y²
dy/dx = 9x² / 12y²
dy/dx = 3x² / 4y²
y' = 3x² / 4y²
2. Determination of y''
To obtain y'', we simply defferentiate above expression i.e y' = 3x² / 4y². This can be obtained as follow:
3x² / 4y²
Let:
u = 3x²
v = 4y²
Find u' and v'
u' = 6x
v' = 8ydy/dx
Applying quotient rule
y'' = [vu' – uv'] / v²
y'' = [4y²(6x) – 3x²(8ydy/dx)] / (4y²)²
y'' = [24xy² – 24x²ydy/dx] / 16y⁴
Recall:
dy/dx = 3x² / 4y²
y'' = [24xy² – 24x²y (3x² / 4y² )] / 16y⁴
y'' = [24xy² – 18x⁴/y] / 16y⁴
y'' = 1/16y⁴[24xy² – 18x⁴/y]
y'' = 1/16y⁴[(24xy³ – 18x⁴)/y]
y'' = 1/16y⁵[(24xy³ – 18x⁴)]
y'' = 6x/16y⁵[(4y³ – 3x³)]
y'' = 3x/8y⁵[(4y³ – 3x³)]
A. Multiplication is the ONLY function that reverses what division did. If you did 56/-14 = n, then n x -14 should equal 56.
Answer:
8.40049 × 10^7
Step-by-step explanation:
Answer:
y = 6x
Step-by-step explanation:
For a vertical stretch, you simply multiply x by the factor you want to stretch it by. 3x • 2 is 6x.
<h2>22</h2>
In this problem, we need to use <u>multiplication</u> and <u>subtraction</u> method to solve it.
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x(y) means to <u>multiply</u> x with y
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Note that {a = 7} and {b = 6}
First, we need to multiply 4 with {a = 7}, we get:
4(7) = <em>28</em>
<em />
Then, we need to subtract {b = 6} from <em>28</em>, we get:
<em>28</em> – 6 = 22
Finally, this simplifies as:
4(7) – 6 = 22
<em>Hope this helps :)</em>
