Calculus Derivatives Quiz

Determine the derivative of the following functions using the definition of the derivative: \( f(x) = x^2 + 2x + 1 \).

Determine the derivative of the following functions using the definition of the derivative: \( f(x) = \sqrt{x+2} \).

Using the rules, determine the derivative of the following: \( y = x \).

Using the rules, determine the derivative of the following: \( y = 1 \).

Using the rules, determine the derivative of the following: \( y = \frac{1}{x^2} \).

Using the rules, determine the derivative of the following: \( y = -4\sqrt{x} \).

Using the rules, determine the derivative of the following: \( y = \frac{-4}{\sqrt{x}} \).

Using the rules, determine the derivative of the following: \( y = \frac{x-1}{3} + \frac{x^2}{x} \).

Using the rules, determine the derivative of the following: \( y = x^3 + \frac{1}{x^2} \).

Using the rules, determine the derivative of the following: \( y = 3x^2 + \frac{2}{x} + \frac{1}{x^2} \).