Calculus Derivatives and Rules

This video tutorial introduces derivative rules, focusing on polynomial functions. It covers the constant rule, power rule, constant multiple rule, and sum and difference rule. The tutorial includes practice problems and demonstrates how to apply derivatives to find tangent lines to curves, emphasizing the practical applications of derivatives in understanding the rate of change.

What is the derivative of a constant function?

• The constant times x

• One

• Zero

• The constant itself

How do you apply the power rule to find the derivative of x^n?

• Multiply n by x^(n-1)

• Subtract 1 from the coefficient

• Add 1 to the exponent

• Multiply n by x^n

What does the constant multiple rule state?

• The derivative of a constant is zero

• Multiply the constant by the derivative of the function

• Add the constant to the derivative

• Divide the constant by the derivative

How do you find the derivative of a sum of functions?

• Add the terms and then differentiate

• Differentiate each term separately and add them

• Subtract the derivatives of each term

• Multiply the derivatives of each term

What is the derivative of x^(1/3) using the power rule?

• x^(1/3)

• 3 x^(1/3)

• 1/3 x^(-2/3)

• 1/3 x^(2/3)

How can you express a negative exponent in a positive form?

• Subtract 1 from the exponent

• Move the term to the denominator

• Add 1 to the exponent

• Multiply by x

What is the derivative of -1/x^5 using the power rule?

• -1/x^5

• 1/x^5

• -5/x^6

• 5/x^6

What is the purpose of finding the equation of a tangent line?

• To calculate the area under the curve

• To find the maximum value of a function

• To find the y-intercept of the function

• To determine the slope at a specific point

How do you find the slope of a tangent line using derivatives?

• Multiply the derivative by x

• Integrate the function

• Find the second derivative

• Evaluate the derivative at the given x-value

What is the equation of a line in slope-intercept form?

• y = mx^2 + b

• y = ax^2 + bx + c

• y = x^2 + c

• y = mx + b