Some problems provide the opportunity for more than one mistake.

The Goal

Find

The Mistakes

Find the mistakes:

1.

Need a hint? Look carefully at the red part:

2.

Need a hint? Look carefully at the red part:

3.

Need a hint? Look carefully at the red part:

A Correct Solution

Explanations

In both cases the formula for the derivative is wrong. Basic derivative formulas should be learned. For secant there are two choices: memorize the correct derivative (try the flashcards at Calculus Facts); or derive the derivative using the definition of secant whenever the derivative of secant is needed:

(Note the use of the chain rule in the derivative step.)

The third mistake is one of notation - perhaps from misunderstanding function notation, or perhaps from laziness. "sec" by itself as notation has no meaning in this context without a specified input (or argument), and certainly the symbol "sectan(x)" is not standard usage for the product of the two function values sec(x)tan(x).