Calculus Derivatives and Expressions

This video tutorial covers higher-order derivatives, focusing on finding first and second derivatives using the power rule, chain rule, and product rule. It includes algebraic simplification techniques and emphasizes the importance of understanding different differentiation rules. The tutorial concludes with a comprehensive example that combines these concepts.

What is the first step in finding the derivative of a function involving a square root?

• Convert to logarithmic form

• Apply the chain rule

• Rewrite the square root as a rational exponent

• Use the product rule

When applying the power rule, what is the derivative of x to the power of 1/2?

• x^(-1/2)

• 2x^(1/2)

• x^(1/2)

• 1/2 x^(-1/2)

In Leibniz's notation, what does dy/dx represent?

• The integral

• The limit

• The first derivative

• The second derivative

What rule is used when differentiating a product of two functions?

• Chain rule

• Quotient rule

• Product rule

• Power rule

What is the derivative of 2x + 5?

• 5

• 2

• 7

• 0

What is the result of multiplying 4 by 2 in the context of the derivative problem?

• 12

• 10

• 8

• 6

What is a common factor in the expression x^2 + 5x?

• x^2 + 5x

• 5x

• x^2

• x + 5

What is the final form of the expression after combining like terms?

• 14x^2 + 70x + 75

• 12x^2 + 60x + 50

• 16x^2 + 80x + 100

• 10x^2 + 50x + 25

What is the purpose of factoring out common factors in an expression?

• To simplify the expression

• To find the derivative

• To change the variable

• To increase complexity

What is the derivative of a constant term?

• One

• Zero

• Undefined

• The constant itself