Calc I - Written HW

Deriving differentiation rules from the definition

Here are a couple of HW problems from Wed, Jan 29. Note that these are not to be collected; they are practice problems to help you do well on our next exam, which is next Fri, Feb 7.

  1. Assuming that \(f\) and \(g\) are differentiable function, use the definition of the derivative to show that \[\frac{d}{dx} (2f(x)) - 3g(x)) = 2f'(x) - 3g'(x).\]

  2. Use the definition of the derivative to show that \[\frac{d}{dx} x^5 = 5x^4.\]

Comments

These problems are not meant to illustrate the use of the differentiation rules; rather, they are meant to help us understand why the differentiation rules are true.

Here are two videos that parallel trickiest parts of our class lecture fairly closely: