Answer:
[tex]\displaystyle \frac{d}{dx} = 2 \cos x - \sec^2 x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 2 \sin x - \tan x[/tex]
Step 2: Differentiate
- Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx} = \frac{d}{dx}[2 \sin x] - \frac{d}{dx}[\tan x][/tex]
- Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} = 2\frac{d}{dx}[\sin x] - \frac{d}{dx}[\tan x][/tex]
- Trigonometric Differentiation: [tex]\displaystyle \frac{d}{dx} = 2 \cos x - \sec^2 x[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
