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Alexandra [31]
2 years ago
14

Find the area of a square with the side lengths of (1/2x+2)

Mathematics
1 answer:
Pavlova-9 [17]2 years ago
8 0

Answer: There are no like terms

Step-by-step explanation:

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The first derivative of x^2+2y^2=16 is -x/(2y), the second is -(2y^2+x^2)/(4y^3). Find the third implicit derivative of x^2+2y^2
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d²y/dx² = (-2y² − x²) / (4y³)

Take the derivative (use quotient rule and chain rule):

d³y/dx³ = [ (4y³) (-4y dy/dx − 2x) − (-2y² − x²) (12y² dy/dx) ] / (4y³)²

d³y/dx³ = [ (-16y⁴ dy/dx − 8xy³ − (-24y⁴ dy/dx − 12x²y² dy/dx) ] / (16y⁶)

d³y/dx³ = (-16y⁴ dy/dx − 8xy³ + 24y⁴ dy/dx + 12x²y² dy/dx) / (16y⁶)

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Substitute:

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d³y/dx³ = ((2y² + 3x²) (-x) − 4xy²) / (8y⁵)

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