If f(x) = 6 sin¯¹(x²), find ƒ'(x). Find ƒ'(0.5).

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Differentiation Exercise**

Given the function:
\[ f(x) = 6 \sin^{-1}(x^2) \]
find the derivative \( f'(x) \).

\[ \boxed{\text{}} \]

Next, calculate the derivative at \( x = 0.5 \).

\[ \boxed{\text{}} \]

**Explanation:**

To solve this problem, we need to find the derivative of the given function and then evaluate it at \( x = 0.5 \). The process involves applying differentiation techniques, which may include the chain rule.
Transcribed Image Text:**Differentiation Exercise** Given the function: \[ f(x) = 6 \sin^{-1}(x^2) \] find the derivative \( f'(x) \). \[ \boxed{\text{}} \] Next, calculate the derivative at \( x = 0.5 \). \[ \boxed{\text{}} \] **Explanation:** To solve this problem, we need to find the derivative of the given function and then evaluate it at \( x = 0.5 \). The process involves applying differentiation techniques, which may include the chain rule.
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