Calculus I: Derivatives of Polynomials and Natural Exponential Functions (Level 2 of 3)

The video tutorial covers advanced differentiation rules, including the constant multiple, sum, and difference rules. It provides geometric interpretations and examples to illustrate these rules. The tutorial also demonstrates how to apply these rules to differentiate more complex functions, combining them with the power rule and natural exponential function derivatives.

What does the constant multiple rule state about the derivative of a constant times a function?

• The derivative is zero.

• The constant is added to the derivative.

• The constant is multiplied by the derivative of the function.

• The constant is subtracted from the derivative.

How can the sum rule be described in terms of derivatives?

• The derivative of a sum is the difference of the derivatives.

• The derivative of a sum is the quotient of the derivatives.

• The derivative of a sum is the product of the derivatives.

• The derivative of a sum is the sum of the derivatives.

Which rule would you apply to find the derivative of a function like 4/3πr³?

• Difference rule

• Sum rule

• Constant multiple rule

• Quotient rule

In the example of finding the derivative of 5x - 1, what is the derivative of the constant term?

• 1

• -1

• 5

• 0

What is the derivative of the function 5x^8 - 2x^5 + 6?

• 40x^6 - 10x^3

• 40x^8 - 10x^5

• 40x^7 - 10x^4

• 40x^7 + 10x^4

When finding the derivative of a function with a square root, what is the first step?

• Differentiate directly

• Apply the sum rule

• Use the quotient rule

• Rewrite the square root as a fractional power

What is the derivative of e^t/3?

• 3e^t

• e^t/3

• e^t

• e^t/9