Problem 11: Chain Rule


Calculate the derivative of tan2(2x –1) with respect tox using the chain rule, and then verify your answer using a second differentiation technique.


Note that tan2(2x –1) = [tan (2x – 1)]2. To apply the chain rule, complete these steps:

  1. Apply the power rule, changing the exponent of 2 into the coefficient of tan (2x – 1), and then subtracting 1 from the square.
  2. Multiply by the expression tan (2x – 1), which was originally raised to the second power.
  3. Take the derivative of tan (2x – 1) with respect to x.
  4. Multiply by the derivative of 2x – 1, the expression that is plugged into tangent.

These four steps are implemented in the solution below.


To verify the derivative, apply the product rule, noting that  tan2(2x –1) = tan (2x –1) · tan (2x – 1). Evev the product rule will require the chain rule, when you differentiate each factor (2x – 1), as demonstrated below.


Both techniques result in the same derivative.

The video may take a few seconds to load. Having trouble Viewing Video content? Some browsers do not support this version - Try a different browser.

Leave a Reply

Your email address will not be published. Required fields are marked *