If y = sec(3x), dy/dx = ?

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Study for the AP Calculus BC Test. Discover flashcards and multiple choice questions with hints and explanations to prepare effectively. Ace your exam!

Multiple Choice

If y = sec(3x), dy/dx = ?

Explanation:
When differentiating secant of a inner function, use the chain rule: d/dx [sec(u)] = sec(u) tan(u) · du/dx. Here u = 3x, so du/dx = 3. Put it together: dy/dx = 3 sec(3x) tan(3x). The 3 comes from the inner function 3x, and the derivative of sec is sec times tan. The other forms would come from misapplying the derivative rules for tan or cosecant, or dropping the inner-derivative factor.

When differentiating secant of a inner function, use the chain rule: d/dx [sec(u)] = sec(u) tan(u) · du/dx. Here u = 3x, so du/dx = 3. Put it together: dy/dx = 3 sec(3x) tan(3x). The 3 comes from the inner function 3x, and the derivative of sec is sec times tan. The other forms would come from misapplying the derivative rules for tan or cosecant, or dropping the inner-derivative factor.

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