Question

Given w(x) = cos(2-3x), which of the following represents w'(x)?

A) sin(2-3x)
B) -3sin(2-3x)
C) -3cos(2-3x)
D) -2sin(2-3x)

Answer 1

The derivative of w(x) = cos(2-3x) is found using the chain rule, resulting in w'(x) = -3sin(2-3x), which corresponds to option B.

Step-by-step explanation:

To determine w'(x) for the function w(x) = cos(2-3x), we can use the chain rule of differentiation. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function.

For w(x) = cos(2-3x), the outer function is cos(u), where u = 2 - 3x. The derivative of cos(u) with respect to u is -sin(u). Since u = 2 - 3x, we then multiply by the derivative of u with respect to x, which is -3.

The resulting derivative, w'(x), is therefore -3sin(2-3x), which corresponds to option B.