Question

Find the derivative of
f(x)=(arccost)second power

Answer 1

`\displaystyle f'(t) = (-2 \arccos t)/(√(1 - t^2))`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
`\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)`

Explanation:

Step 1: Define

Identify

`\displaystyle f(t) = (\arccos t)^2`

Step 2: Differentiate

1. Basic Power Rule [Derivative Rule - Chain Rule]:
   `\displaystyle f'(t) = 2 \arccos t (\arccos t)'`
2. Trigonometric Differentiation:
   `\displaystyle f'(t) = (-2 \arccos t)/(√(1 - t^2))`

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation