Question

Find the derivative of the trigonometric function y = 3 sin(2x).

a) 6 cos(2x)
b) 3 cos(2x)
c) 6 sin(2x)
d) 3 sin(2x)

Answer 1

The derivative of y = 3 sin(2x) is found by applying the chain rule to the trigonometric function, resulting in the correct answer of 6 cos(2x). option a is correct answer.

Step-by-step explanation:

The question asks us to find the derivative of the trigonometric function y = 3 sin(2x). In calculus, the process of finding a derivative is used to determine the rate of change of one quantity with respect to another. Specifically, for trigonometric functions, there are standard rules that we apply. The derivative of sin(u) with respect to x is cos(u) multiplied by the derivative of u with respect to x.

1. First, we recognize that the function we have is of the form f(x) = asin(bx), where a is a constant scalar and b is a constant that multiplies the variable x.
2. Apply the chain rule: The derivative of f(x) with respect to x is ab cos(bx).
3. For our specific function y = 3 sin(2x), this means the derivative is 6 cos(2x), because a is 3 and b is 2, and the derivative of 2x with respect to x is simply 2.

Therefore, the correct answer is a) 6 cos(2x).