Implicit Differentiation Quiz

Why is implicit differentiation necessary for certain equations?

• Because they are not explicitly in terms of x.

• Because they are quadratic equations.

• Because they have no x terms.

• Because they are linear equations.

What must you remember when differentiating a y term?

• Multiply by dy/dx after the term.

• Divide by dx/dy after the term.

• Add dx/dy after the term.

• Subtract dy/dx from the term.

What is the first step in differentiating the term x^3?

• Subtract 1 from the exponent.

• Divide the exponent by x.

• Multiply the exponent by x.

• Add 1 to the exponent.

When using the product rule, what is the formula used?

• First term times second term.

• First term times derivative of second term plus derivative of first term times second term.

• First term plus second term.

• Derivative of first term plus derivative of second term.

What is the derivative of a constant, such as 5?

• 0

• 5

• Undefined

• 1

What is the next step after differentiating all terms in the equation?

• Solve for dy/dx.

• Solve for y.

• Solve for dx/dy.

• Solve for x.

How do you isolate dy/dx in the equation?

• Multiply all terms by dy/dx.

• Factor out dy/dx.

• Add all terms to one side.

• Subtract dy/dx from all terms.

What is the final step to solve for dy/dx?

• Divide both sides by the remaining terms.

• Multiply both sides by dy/dx.

• Subtract dy/dx from both sides.

• Add dy/dx to both sides.

What is the solution for dy/dx in the given problem?

• 3x^2 + 2xy / 3y^2 - x^2

• -3x^2 + 2xy / -3y^2 - x^2

• -3x^2 - 2xy / -3y^2 + x^2

• 3x^2 - 2xy / 3y^2 + x^2

What is the main takeaway from the video on implicit differentiation?

• Implicit differentiation is not useful for complex equations.

• Implicit differentiation is similar to explicit differentiation but requires handling y terms differently.

• Implicit differentiation is only used for solving quadratic equations.

• Implicit differentiation is only for linear equations.