Understanding Derivatives

What is the derivative of a function f with respect to x called?

• f prime

• f inverse

• f double prime

• f integral

What is the derivative of f(x) = x^2?

• 2x^2

• x^2

• 2x

• x

When finding the derivative of f(x) = x^2, what happens to the x^2 terms in the limit process?

• They add up

• They cancel each other out

• They multiply

• They remain unchanged

What is the alternate definition of a derivative used for?

• Finding the integral

• Finding the minimum value

• Finding the maximum value

• Finding the derivative at a specific point

What is the purpose of rationalizing the numerator when finding the derivative of f(x) = √x?

• To simplify the limit process

• To find the integral

• To change the function

• To eliminate the variable

What is the result of rationalizing the numerator for the function f(x) = √x?

• x + a

• 2x

• x - a

• 1 over 2√a

Which notation for derivatives emphasizes the operation being performed on a function?

• f prime

• y prime

• d/dx of f(x)

• f double prime

What does the notation dy/dx represent?

• The inverse of y

• The square of y

• The integral of y with respect to x

• The derivative of y with respect to x

Which notation for derivatives names both the dependent and independent variables?

• f double prime

• y prime

• f prime

• dy/dx

What is the advantage of using the notation df/dx?

• It emphasizes the function name

• It is less common

• It is shorter

• It is more complex