Implicit Differentiation Quiz

What is the derivative of sin(x) with respect to x?

• -sin(x)

• -cos(x)

• sin(x)

• cos(x)

In implicit differentiation, what additional step is needed when differentiating a function of y?

• Subtract dy/dx

• Add dy/dx

• Multiply by dy/dx

• Multiply by dx/dy

What is the equation of a circle with radius 5 centered at the origin?

• x^2 - y^2 = 5

• x^2 + y^2 = 25

• x^2 + y^2 = 5

• x^2 - y^2 = 25

When using implicit differentiation on x^2 + y^2 = 25, what is the derivative of y^2?

• 2y dy/dx

• 2y

• 2x dy/dx

• 2x

What is the result of differentiating x^3 with respect to x?

• x^3

• 3x

• 3x^2

• x^2

In the equation x^3 + y^3 = 2xy, what rule is used to differentiate the right side?

• Chain rule

• Product rule

• Quotient rule

• Power rule

What is the derivative of y^2 with respect to x using implicit differentiation?

• 2y

• 2y dy/dx

• 2x

• 2x dy/dx

In the equation x^2y + xy^2 = 6, what is the derivative of the term x^2y using the product rule?

• 2x + y

• x^2 + 2y

• 2xy + y^2

• 2xy + x^2 dy/dx

What is the final expression for dy/dx in the equation x^2y + xy^2 = 6 after implicit differentiation?

• (2xy + y^2) / (x^2 + 2xy)

• (2xy - y^2) / (x^2 - 2xy)

• (2xy - y^2) / (x^2 + 2xy)

• (2xy + y^2) / (x^2 - 2xy)

What is the slope of the tangent line to the equation x^2y + xy^2 = 6 at the point (-3, 1)?

• -5/3

• 5/3

• -3/5

• 3/5