Common Calculus Mistakes
Derivatives of Trigonometric Functions: Secant 
Some problems provide the opportunity for more than one mistake. The Goal
Find
The Mistakes
Find the mistakes:
(Roll the mouse over the math to see a hint in red)
(Roll the mouse over the math to see a hint in red)
(Roll the mouse over the math to see a hint in red) A Correct Solution
(Roll the mouse over the area above to see the corrections in blue) 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). 
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