Understanding Derivatives and Power Rule

The video tutorial explains how to find the derivative of a function involving a cube root by rewriting it using exponent rules and applying the power rule. The function is rewritten as x to the 1/3 power, allowing the power rule to be applied. The derivative is calculated and evaluated at a specific point, with the result simplified using exponent properties. The tutorial encourages reviewing exponent properties if needed.

What is the initial function given in the problem?

• f(x) = 4 * x^3

• f(x) = -4 * x^2

• f(x) = 4 * square root of x

• f(x) = -4 * cube root of x

How can the cube root of x be expressed using exponents?

• x^1

• x^2

• x^(1/3)

• x^(3/2)

What is the purpose of rewriting the function using exponent notation?

• To graph the function

• To make it easier to integrate

• To apply the power rule

• To solve a quadratic equation

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

• Subtract 1 from the coefficient

• Divide the coefficient by the exponent

• Add 1 to the exponent

• Multiply the exponent by the coefficient

What is the derivative of the function after applying the power rule?

• -4/3 * x^(-2/3)

• 4/3 * x^(2/3)

• 4 * x^(-1/3)

• -4 * x^(1/3)

What is the value of 8 raised to the power of 1/3?

• 1

• 2

• 4

• 8

How is 2 raised to the power of -2 expressed as a fraction?

• 1/4

• 2/1

• 4/1

• 1/2

What is the final simplified value of the derivative at x = 8?

• 1/3

• 1/4

• 3/4

• 2/3

What mathematical concept is used to simplify the expression 8^(1/3) raised to the -2 power?

• Exponent properties

• Logarithms

• Algebraic identities

• Trigonometry

Which online platform is recommended for reviewing exponent properties?

• Coursera

• Khan Academy

• edX

• Udemy