Calculus I: Derivatives of Polynomials and Natural Exponential Functions (Level 1 of 3)

The video tutorial introduces derivative rules for polynomials and natural exponential functions, focusing on simplifying the process without using the definition of derivatives. It covers the derivative of constant functions, the power rule, and the derivative of natural exponential functions. The tutorial includes examples to illustrate these rules, demonstrating how to find derivatives of various functions, including constant, power, and exponential functions.

What is the derivative of a constant function?

• It is equal to zero.

• It is equal to one.

• It is undefined.

• It is equal to the constant itself.

According to the power rule, what is the derivative of x^n?

• n * x^(n+1)

• x^n

• n * x^(n-1)

• n * x^n

What is the derivative of the function f(x) = x?

• x

• 1

• x^2

• 0

What is the derivative of the natural exponential function e^x?

• 0

• e^x

• x * e^x

• e^(x-1)

How is the derivative of e^x related to the function itself?

• It is equal to the function itself.

• It is the inverse of the function.

• It is the square of the function.

• It is the reciprocal of the function.

What is the derivative of f(x) = 10?

• 0

• x

• 10

• 1

Using the power rule, what is the derivative of f(x) = x^3?

• x^3

• 3x^3

• x^2

• 3x^2

How can the function f(x) = 1/x^2 be rewritten to apply the power rule?

• x^-2

• x^2

• 1/x

• x^3

What is the derivative of f(x) = sqrt(x)?

• 2sqrt(x)

• x^(1/2)

• 1/(2sqrt(x))

• sqrt(x)

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

• x * e^x

• 0

• e^x

• e^(x-1)