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Evgesh-ka [11]
3 years ago
5

I need some help with this calculus 1 implicit diffrention problem?

Mathematics
1 answer:
katen-ka-za [31]3 years ago
7 0

Answer:

y" = -24 / y³

Step-by-step explanation:

6x² + y² = 4

Take the derivative of both sides with respect to x.

12x + 2y y' = 0

Again, take the derivative of both sides with respect to x.

12 + 2y y" + y' (2y') = 0

12 + 2y y" + 2(y')² = 0

Solve for y' in the first equation.

2y y' = -12x

y' = -6x/y

Substitute and solve for y":

12 + 2y y" + 2(-6x/y)² = 0

12 + 2y y" + 2(36x²/y²) = 0

12 + 2y y" + 72x²/y² = 0

6y² + y³ y" + 36x² = 0

y³ y" = -36x² − 6y²

y" = (-36x² − 6y²) / y³

Solve for y² in the original equation and substitute:

y² = 4 − 6x²

y" = (-36x² − 6(4 − 6x²)) / y³

y" = (-36x² − 24 + 36x²) / y³

y" = -24 / y³

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A² + b² = 7b and b² + (2b-a)² = 7² find (a - b)².
Mamont248 [21]

Answer:

(a - b)^2 = 49 - 4b^2 +2ab

Step-by-step explanation:

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Find; (a - b)^2

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Start with b^2 + (2b - a)^2 = 7^2 =>

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a^2 + b^2 + 4b^2 - 4ab = 49 rearranging terms

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Double Check: recalculated ✅ ✅

(a - b)^2 = 49 - 4b^2 +2ab

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