Implicit differentiation

What is the derivative dy/dx of the equation x^3 + y^3 = 8?

• -x^2/y^2

• x^2/y^2

• -3x^2/3y^2

• 3x^2/3y^2

Find dy/dx for the equation x^2 + 2xy + y^2 = 5.

• (x+y)/(x+y)

• -(x+y)/(x+y)

• -1

• 1

Determine dy/dx for the equation 5xy - y^3 = 8.

• (5y)/(5x - 3y^2)

• (-5y)/(5x - 3y^2)

• (5y)/(3y^2 - 5x)

• (-5y)/(3y^2 - 5x)

What is the derivative dy/dx of the equation tan(xy) = 7?

• y/x

• -y/x

• x/y

• -x/y

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What is the first derivative, dy/dx, of the equation tan(xy) = 7?

• y/x

• -y/x

• x/y

• -x/y

Before differentiating 36 = sqrt(x^2 + y^2), what is the simplified form of the equation after squaring both sides?

• 36 = x + y

• 1296 = x^2 + y^2

• 36^2 = x^2 - y^2

• 1296 = (x+y)^2

Determine the first derivative, dy/dx, of the equation 36 = sqrt(x^2 + y^2).

• x/y

• y/x

• -x/y

• -y/x

What is the second derivative, d^2y/dx^2, of the equation 36 = sqrt(x^2 + y^2)?

• -(x^2 + y^2) / y^3

• (x^2 + y^2) / y^3

• -(x^2 - y^2) / y^3

• (x^2 - y^2) / y^3