Derivatives and Power Rule Concepts

The video tutorial explains how to find the derivative of functions using the power rule of differentiation. It begins by rewriting functions into a form suitable for applying the power rule. The tutorial then demonstrates the process of finding the derivatives of two functions, F(x) and G(x), by applying the power rule and simplifying the results.

What is the first step in applying the power rule to a function?

• Add one to the exponent

• Divide the coefficient by the exponent

• Rewrite the function in a suitable form

• Multiply the exponent by the coefficient

How is the function 4 divided by X cubed rewritten using the power rule?

• 4x^3

• 4x^-3

• 4/x^3

• 4x^2

What is the derivative of 4x to the power of negative three?

• -12x^4

• 12x^4

• 12x^-4

• -12x^-4

How can the derivative of 4x^-3 be expressed in a different form?

• -12/x^4

• 12/x^4

• -12x^4

• 12x^4

What is the derivative of 3x to the power of negative one half?

• -3/2x^-3/2

• 3/2x^3/2

• 3/2x^-3/2

• -3/2x^3/2

How can the derivative of 3x^-1/2 be rewritten?

• 3/2x^3/2

• -3/2x^3/2

• -3/2x^-3/2

• 3/2x^-3/2