Differentiation Techniques and Applications

The video tutorial explains how to find the derivative of a function using implicit differentiation. It starts with a given equation and demonstrates the process of differentiating both sides with respect to x. The tutorial covers the application of the product rule and solving for dy/dx. Finally, it evaluates dy/dx at a specific point using provided values, illustrating the complete process of implicit differentiation.

What is the initial equation given in the problem?

• 3x^2 + 5x = 5

• 3x^2 + 5x + xy = 5

• 5x + xy = 5

• 3x^2 + xy = 5

What method is used to find y' at x=5?

• Explicit differentiation

• Implicit differentiation

• Graphical differentiation

• Numerical differentiation

What rule is applied when differentiating the term xy?

• Quotient rule

• Product rule

• Power rule

• Chain rule

What is the derivative of 3x^2 with respect to x?

• 3x

• 9x

• 6x

• x^2

What is the derivative of 5x with respect to x?

• 1

• x

• 0

• 5

After applying the product rule, what expression represents the derivative of xy?

• x + y

• dy/dx + y

• x(dy/dx) + y

• x + dy/dx

What is the simplified form of dy/dx after isolating terms?

• -6x + y + 5

• 6x + y + 5

• -6x - y - 5

• 6x - y - 5

What values are substituted for x and y to find y' at x=5?

• x=5, y=9

• x=5, y=-19

• x=9, y=5

• x=-19, y=5

What is the final value of y' at x=5?

• 5

• -5

• 16

• -16

What is the derivative of a constant, such as 5, with respect to x?

• x

• 1

• 0

• 5