Derivative Shortcut Rules Quiz

What is the power rule used for in calculus?

• Finding the limit of a function

• Finding the derivative of a constant

• Finding the integral of a function

• Finding the derivative of a function where the variable is the base and the exponent is a constant

If you have a function f(x) = x^5, what is the derivative using the power rule?

• 5x^4

• x^4

• 5x^5

• x^5

How can you express the derivative of 1/x using the power rule?

• -x^2

• x^2

• 1/x^2

• -1/x^2

What is the derivative of the square root of x using the power rule?

• 1/(2√x)

• 2√x

• 1/√x

• √x

How do you express the cube root of x as a power?

• x^(1/3)

• x^(-1/3)

• x^3

• x^(1/2)

What does the sum and difference rule allow you to do?

• Multiply each term of an expression separately

• Find the limit of each term of an expression separately

• Integrate each term of an expression separately

• Differentiate each term of an expression separately

What is the derivative of x^4 + x^2 using the sum and difference rule?

• x^3 + x

• 4x^3 + x^2

• 4x^3 + 2x

• 4x^4 + 2x^2

What is the constant multiple rule in calculus?

• The derivative of a constant is zero

• The derivative of a constant times a function is the constant times the derivative of the function

• The integral of a constant is zero

• The limit of a constant is zero

How does the constant multiple rule differ from the derivative of a constant?

• Both are the same

• The constant multiple rule results in zero

• The derivative of a constant is always one

• The constant multiple rule involves a constant times a function, while the derivative of a constant is zero

What is the derivative of 3x^4 using the constant multiple rule?

• 12x^3

• 3x^3

• 12x^4

• 3x^4