Peer Review Question

Posted on March 6, 2014 by Ismail Akram

Sample peer review Q for the test.

Is the derivative of a product the same as product of the derivatives?

i.e. it is true that

\frac{d}{dx}\left(f\left(x\right)g\left(x\right)\right)=f'\left(x\right)g'\left(x\right)?

Find a counterexample:

(aka Prove the product rule).

-Izzy

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One Response to Peer Review Question

  1. Kate Poirier says:
    March 6, 2014 at 12:29 pm

    Nice question Izzy! I especially like that you asked for a counterexample. Proving the product rule in general (using the limit definition) was a fun in-class activity (for me anyway!), but it might not be the most appropriate test question, just because you have to remember that one clever trick.

    Your questions made me think of something we did talk about briefly in class:

    Can you find two functions f(x) and g(x) so that the derivative is the product IS the product of the derivatives? We talked about some easy examples of f(x) and g(x)…are there any non-obvious examples? Why or why not?

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