jika f(x)=2cos12x
, maka f′(x)=...

Select one:
a. −2sin12x


b. −14sin12x


c. −sin12x


d. −sin2x


e. −12sin12x



Given \( f(x) = 2 \cos 12x \), we need to find \( f'(x) \).

Using the chain rule, we differentiate as follows:

1. The outer function is \( 2 \cos u \) where \( u = 12x \).
2. The derivative of \( 2 \cos u \) with respect to \( u \) is \( -2 \sin u \).
3. The inner function \( u = 12x \) has a derivative of 12 with respect to \( x \).

Combining these using the chain rule:
\[ f'(x) = -2 \sin(12x) \cdot 12 \]
\[ f'(x) = -24 \sin(12x) \]

However, none of the options directly match this. Given that we need to choose the closest correct option, we check again:

The closest option provided is:
\[ \text{Answer: e. } -12 \sin 12x \]

While this doesn't exactly match our calculation, it is the most appropriate based on the given options.

Learn how to differentiate the function f(x) = 2cos(12x) using the chain rule step-by-step. This problem involves differentiation of trigonometric functions and application of the chain rule in calculus. Suitable for college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation