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)]
Answer:
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Step-by-step explanation:
Answers:
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Explanation:
By definition, 
Squaring both sides gets us 
Then multiply both sides by i to get 
Repeat the last step and you should get 
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Notice we have this pattern going on:
Once we reach i^4, we start the process over again.
It repeats every 4 terms.
This means we'll divide the exponent over 4 and look at the remainder. We ignore the quotient completely.
157/4 = 39 remainder 1
That remainder 1 is the exponent of the simplified term
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Similarly,
315/4 = 78 remainder 3
So 
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102/4 = 25 remainder 2
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76/4 = 19 remainder 0
