Calculating Derivatives and Power Rule

This video tutorial covers the basics of derivatives in calculus, focusing on solving derivatives of different expressions using a generic formula. It includes three examples: the derivative of 7/U, the derivative of the square root of 3x, and the derivative of 6x^3 - 12x. Each example is explained step-by-step, demonstrating how to apply the formula and simplify the results. The video emphasizes the importance of understanding the process and provides tips for simplifying expressions.

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What is the generic formula used for finding the derivative of ax^b?

• a * b * x^(b+1)

• b * x^(a-1)

• a * x^b

• a * b * x^(b-1)

How is the expression 7/U rewritten to apply the power rule?

• 7U^1

• 7U^-1

• 7U^0

• 7U^2

What is the derivative of 7/U with respect to U?

• 7U^2

• -7U^2

• 7U^-2

• -7U^-2

How is the square root of 3x expressed in terms of exponents?

• 3x^1

• 3x^0.5

• 3x^2

• 3x^-0.5

What is the derivative of the square root of 3x?

• sqrt(3)/2 * x^(-0.5)

• sqrt(3)/2 * x^(0.5)

• 3/2 * x^(0.5)

• 3/2 * x^(-0.5)

What is the first step in finding the derivative of 6x^3 - 12x?

• Combine the terms

• Simplify the expression

• Apply the power rule to each term separately

• Factor out the common terms

What is the derivative of 6x^3?

• 18x^2

• 6x^2

• 6x^3

• 18x^3

What is the derivative of 12x?

• 12

• 0

• 12x

• x

What is the final derivative of the expression 6x^3 - 12x?

• 18x^3 - 12x

• 6x^2 - 12

• 6x^3 - 12

• 18x^2 - 12