Question

Value of the derivative of g(x)=8-10Cosx at 'x=0' is?

Answer 1

g'(0) = 0

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Function Notation

Pre-Calculus

• Unit Circle

Calculus

• Derivatives
• Derivative Notation
• The derivative of a constant is equal to 0
• Derivative Property:
  `(d)/(dx) [cf(x)] = c \cdot f'(x)`
• Trig Derivative:
  `(d)/(dx) [cos(x)] = -sin(x)`

Explanation:

Step 1: Define

g(x) = 8 - 10cos(x)

x = 0

Step 2: Differentiate

1. Differentiate [Trig]: g'(x) = 0 - 10[-sin(x)]
2. Simplify Derivative: g'(x) = 10sin(x)

Step 3: Evaluate

1. Substitute in x: g'(0) = 10sin(0)
2. Evaluate Trig: g'(0) = 10(0)
3. Multiply: g'(0) = 0