Question

Find the derivative of 2sinx-tanx

Answer 1

`\displaystyle (d)/(dx) = 2 \cos x - \sec^2 x`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:
`\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)`

Derivative Property [Addition/Subtraction]:
`\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]`

Explanation:

Step 1: Define

Identify

`\displaystyle y = 2 \sin x - \tan x`

Step 2: Differentiate

1. Derivative Property [Addition/Subtraction]:
   `\displaystyle (d)/(dx) = (d)/(dx)[2 \sin x] - (d)/(dx)[\tan x]`
2. Rewrite [Derivative Property - Multiplied Constant]:
   `\displaystyle (d)/(dx) = 2(d)/(dx)[\sin x] - (d)/(dx)[\tan x]`
3. Trigonometric Differentiation:
   `\displaystyle (d)/(dx) = 2 \cos x - \sec^2 x`

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

Unit: Differentiation