Question

If f(x) = cos(√x - ln(x²))³, then f'(x) is equal to:

A) 3(cos(√x - ln(x²))² ⋅ (-1/2x)
B) -3(cos(√x - ln(x²))² ⋅ 1/2x
C) 3(cos(√x + ln(x²))² ⋅ 1/x
D) -3(cos(√x + ln(x²))² ⋅ 1/x

Answer 1

The derivative of the function f(x) = cos(√x - ln(x²))³ is found by applying the chain rule, yielding the answer A) 3(cos(√x - ln(x²))² ⋅ (-1/2x).

Step-by-step explanation:

To find the derivative of f(x) = cos(√x - ln(x²))³, we can use the chain rule. Let's break it down step by step:

1. Differentiate the outer function: 3(cos(√x - ln(x²))²).
2. Multiply by the derivative of the inner function: 3(cos(√x - ln(x²))² × (-1/2x).

Therefore, the correct answer is option A) 3(cos(√x - ln(x²))² × (-1/2x).