Calculus: Derivatives and Functions Quiz

What does the power rule state about the derivative of x raised to the power n?

• n multiplied by x to the power of (n-1)

• n plus x to the power of (n-1)

• x to the power of n divided by n

• n divided by x to the power of (n+1)

What is the derivative of x^1000?

• x^1000/1000

• 999x^1000

• 1000x^1001

• 1000x^999

What is the derivative of an exponential function proportional to?

• The function itself

• The reciprocal of the function

• The logarithm of the function

• The square of the function

What is the derivative of the function e^x?

• e^x - 1

• 1/e^x

• x^e

• e^x

According to the sum rule, how do you find the derivative of the sum of two functions?

• It is the sum of the derivatives of the individual functions

• It is the product of the derivatives of the individual functions

• It is the derivative of the first function minus the derivative of the second function

• It is the integral of the derivatives of the individual functions

How do you find the derivative of a product of a constant and a function?

• Subtract the derivative of the function from the constant

• Add the constant to the derivative of the function

• Divide the constant by the derivative of the function

• Multiply the constant with the derivative of the function

What is the derivative of the function y = 3x^4?

• 12x^3

• 12x^5

• 4x^3

• 3x^3

Where is the tangent line horizontal for the function y = x^4 - 6x^2 + 4?

• x = 1 or x = ±sqrt(2)

• x = 1 or x = ±sqrt(3)

• x = 0 or x = ±sqrt(3)

• x = 0 or x = ±sqrt(2)

What does a positive derivative indicate about the slope of a function?

• The slope is positive

• The function is positive

• The slope is increasing

• The function is linear

What does the derivative f'(x) = e^x - 1 indicate about the function at x = 0?

• The function has a slope of 0

• The function has a slope of e

• The function has a slope of 1

• The function has a slope of -1