Understanding Derivatives

This video tutorial covers the basics of finding derivatives, starting with constants and moving to monomials using the power rule. It explains the constant multiple rule and the limit definition of derivatives. The tutorial also discusses the difference between tangent and secant lines, and how to find the slope of a tangent line. It includes examples of finding derivatives of polynomial, rational, and radical functions. The video concludes with the application of product and quotient rules for derivatives.

What is the derivative of a constant function?

• The constant itself

• The constant times x

• Zero

• One

Using the power rule, what is the derivative of x^3?

• 3x^3

• x^3

• x^2

• 3x^2

How does the constant multiple rule help in finding derivatives?

• It adds the constant to the derivative

• It multiplies the constant by the derivative of the function

• It allows you to ignore constants

• It divides the constant by the derivative

What is the derivative of x^2 using the definition of the derivative?

• 2

• 2x

• x^2

• x

What is the slope of the tangent line to the curve y = x^2 at x = 1?

• 1

• 0

• 2

• 3

How do you find the derivative of 1/x?

• 1/x^2

• -x^2

• x^2

• -1/x^2

What is the derivative of the square root of x?

• 1/(2√x)

• √x

• 2√x

• 1/x

What is the derivative of sin(x)?

• -cos(x)

• tan(x)

• -sin(x)

• cos(x)

Which rule is used to find the derivative of a product of two functions?

• Power Rule

• Quotient Rule

• Product Rule

• Chain Rule

What is the derivative of a quotient of two functions?

• Product Rule

• Chain Rule

• Power Rule

• Quotient Rule