1.6 Derivatives

The use of calculators or other technologies are strictly prohibited for this assignment.

1 Understanding Derivatives as Slopes

  1. The slope of a straight line doesn’t change for any \(x\). What’s the derivative (slope) of the function \(f(x) = 2 x + 3\)?

  2. What’s the derivative (slope) of the function \(f(x) = 0.5 x + 4\)?

2 Derivative of a Constant; Power Rule; Sums Rule

  1. Find the derivative of \(f(x) = x^0\).

  2. Find the derivative of \(f(x) = 2\).

  3. Find the derivative of \(f(x) = 3 x^2\).

  4. Find the derivative of \(f(x) = 4 x^3\).

  5. Find the derivative of \(f(x) = 4 x^3 + 3 x^2\).

  6. Find the derivative of \(f(x) = 4 x^3 + 3\).

3 Derivative of the Natural Log

Find the derivatives of:

  1. Find the derivative of \(f(x) = \ln(x)\).

  2. What is the derivative of \(f(x) = \ln(x)\) evaluated at \(x = 4\)?

  3. Find the derivative of \(f(x) = 3\ln(x)\).