Derivatives of Trig Functions quiz #1 Flashcards
Derivatives of Trig Functions quiz #1
You can tap to flip the card.
Control buttons has been changed to "navigation" mode.
1/10Skip to main content
What is the derivative of f(x) = x^2 sin(x)?
Using the product rule, the derivative is f'(x) = x^2 cos(x) + 2x sin(x). How can you quickly find the 37th derivative of sin(x) without differentiating 37 times?
Divide 37 by 4; the remainder is 1, so the 37th derivative is the same as the first derivative: cos(x). What is the derivative of f(x) = 4x sec(x)?
Using the product rule, the derivative is f'(x) = 4 sec(x) (x tan(x) + 1). What is the derivative of sin(x) with respect to x?
The derivative of sin(x) is cos(x). How do you find the nth derivative of sin(x) or cos(x) quickly?
Divide n by 4 and use the remainder to determine which derivative to take; every 4th derivative returns to the original function. What is the derivative of tan(x) and how can it be derived?
The derivative of tan(x) is sec^2(x), which can be derived using the quotient rule on sin(x)/cos(x). What is the derivative of cot(x) and what pattern do cofunction derivatives follow?
The derivative of cot(x) is -csc^2(x); all cofunction derivatives (like cosine, cotangent, cosecant) are negative. How do you apply the product rule to find the derivative of f(x) = x^2 sin(x)?
Use the product rule: f'(x) = x^2 cos(x) + 2x sin(x). How can you quickly find the 37th derivative of sin(x) without differentiating 37 times?
Divide 37 by 4; the remainder is 1, so the 37th derivative is the same as the first derivative: cos(x). What is the derivative of f(x) = 4x sec(x) using the product rule?
Using the product rule, the derivative is f'(x) = 4 sec(x) (x tan(x) + 1).
03:53
