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

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

A.

B. For example: is a polynomial

Step-by-step explanation:

A.

Degree is the highest power of the exponent in the polynomial.

A third degree polynomial is of form . Its degree is 3.

This polynomial is in standard form as the terms are ordered from the biggest  (3) to the lowest exponent (0).

B.

A polynomial is an expression consisting of variables and coefficients combined together using arithmetic operations. Exponents of variables are non-negative integers.

Polynomials are closed under addition as sum of two polynomial is also a polynomial.

For example: take two polynomials as

Here,

is also a polynomial.