Understanding Derivatives Using the Power Rule

The video tutorial explains how to find the derivative of functions using the power rule of differentiation. It begins by introducing the power rule, which involves multiplying by the exponent and subtracting one from it. The tutorial then demonstrates finding the derivative of f(x) = 4x^3, resulting in 12x^2. Next, it covers the derivative of g(x) = 3√x by expressing the square root as a rational exponent, leading to a derivative of 3/(2√x).

What is the first step in applying the power rule to find the derivative of x^n?

• Multiply by the exponent

• Divide by the exponent

• Add one to the exponent

• Subtract the exponent

When using the power rule, what do you do after multiplying by the exponent?

• Add one to the exponent

• Multiply by the base

• Divide by the base

• Subtract one from the exponent

What is the derivative of f(x) = 4x^3 using the power rule?

• 8x^2

• 12x^2

• 16x^3

• 4x^3

How is the square root of x expressed as a rational exponent?

• x^(-1/2)

• x^(1/2)

• x^1

• x^2

What is the derivative of g(x) = 3√x in terms of rational exponents?

• 3/2x^(1/2)

• 3x^(1/2)

• 3/2x^(-1/2)

• 3x^(-1/2)

How can the derivative of g(x) = 3√x be expressed in terms of square roots?

• 3/√x

• 3/2√x

• 3√x

• 3x/2