Answer:
[tex]\displaystyle y' = - \csc (x) \big[ \cot^2 (x) + \csc^2 (x) \big][/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
Functions
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle y = \csc (x) \cot (x)[/tex]
Step 2: Differentiate
- Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[\csc (x)] \cot (x) + \csc (x) \frac{d}{dx}[\cot (x)][/tex]
- Trigonometric Differentiation: [tex]\displaystyle y' = - \csc (x) \cot (x) \cot (x) + \csc (x) \big[ - \csc ^2 (x) \big][/tex]
- Simplify: [tex]\displaystyle y' = - \csc (x) \cot^2 (x) - \csc^3 (x)[/tex]
- Factor: [tex]\displaystyle y' = - \csc (x) \big[ \cot^2 (x) + \csc^2 (x) \big][/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
