Implicit Differentiation Concepts

This video tutorial covers implicit differentiation, starting with basic concepts and examples. It explains how to find the first and second derivatives using implicit differentiation, including the use of the quotient rule. The tutorial also includes example problems and demonstrates how to apply implicit differentiation to trigonometric functions. Advanced techniques and examples are provided to deepen understanding.

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

• y^2

• 2y * dy/dx

• dy/dx

• 2y

When finding the second derivative in implicit differentiation, which rule is often used?

• Product Rule

• Chain Rule

• Quotient Rule

• Power Rule

In implicit differentiation, what must you remember to add when differentiating a y variable?

• dx/dy

• dy/dx

• d^2y/dx^2

• d^2x/dy^2

How do you find the derivative of a product of x and y in implicit differentiation?

• Use the Quotient Rule

• Use the Product Rule

• Use the Power Rule

• Use the Chain Rule

What is the first step in simplifying expressions with negative exponents in implicit differentiation?

• Multiply by the reciprocal

• Move the term to the denominator

• Add a constant

• Differentiate again

What is the derivative of sin(y) with respect to x in implicit differentiation?

• cos(y)

• cos(y) * dy/dx

• sin(y) * dy/dx

• sin(y)

In implicit differentiation, what is the derivative of cos(xy) with respect to x?

• sin(xy) * (y + x * dy/dx)

• -sin(xy) * (y + x * dy/dx)

• -cos(xy) * (y + x * dy/dx)

• cos(xy) * (y + x * dy/dx)

What is the result of differentiating the equation x^3 - xy + y^2 = 4 implicitly?

• 3x^2 + y + x * dy/dx - 2y * dy/dx = 0

• 3x^2 + y - x * dy/dx - 2y * dy/dx = 0

• 3x^2 - y - x * dy/dx + 2y * dy/dx = 0

• 3x^2 - y + x * dy/dx + 2y * dy/dx = 0

How do you find the first derivative of the equation sqrt(x) + sqrt(y) = 9?

• 1/(2sqrt(x)) - 1/(2sqrt(y)) = 0

• 1/(2sqrt(x)) - 1/(2sqrt(y)) * dy/dx = 0

• 1/(2sqrt(x)) + 1/(2sqrt(y)) * dy/dx = 0

• 1/(2sqrt(x)) + 1/(2sqrt(y)) = 0

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

• cos(x + y) * (1 + dy/dx)

• sin(x + y) * (1 + dy/dx)

• sin(x + y) * (1 - dy/dx)

• cos(x + y) * (1 - dy/dx)