Understanding Derivatives Using the Power Rule

The video tutorial explains the power rule of differentiation, demonstrating how to find the derivative of functions using this rule. It covers examples with coefficients, constants, sums, and differences of terms, and simplifies complex expressions. The tutorial concludes with a preview of upcoming topics on negative and fractional exponents.

What is the derivative of x^n according to the Power Rule?

• n * x^n

• x^n

• n * x^(n-1)

• x^(n-1)

If f(x) = 7x^7, what is f'(x) using the Power Rule?

• 6x^7

• 49x^6

• 7x^6

• 7x^7

How do you find the derivative of a constant multiplied by a function?

• Subtract the constant from the derivative of the function

• Multiply the constant by the derivative of the function

• Divide the constant by the derivative of the function

• Add the constant to the derivative of the function

What is the derivative of -8x^3?

• -24x^3

• -8x^3

• -8x^2

• -24x^2

When applying the Power Rule to a sum of terms, what should you do?

• Apply the Power Rule to each term separately

• Add the exponents of each term

• Subtract the exponents of each term

• Multiply the coefficients of each term

What is the derivative of x^4 - 5x^2?

• 4x^3 - 5

• 4x^3 - 10x

• 4x^3 - 5x

• x^3 - 10x

How do you handle the derivative of a constant term?

• The derivative is the constant itself

• The derivative is 0

• The derivative is 1

• The derivative is undefined

What is the derivative of 1/8 * x^4?

• 1/2 * x^4

• 1/8 * x^3

• 1/2 * x^3

• 1/8 * x^4

What is the derivative of 2x?

• 1

• 0

• x

• 2

What will be covered in the next part of the tutorial?

• Trigonometric functions

• Integration techniques

• Negative and fractional exponents

• Advanced algebra