Find an equation of the line tangent to the curve y = sin x at x = 0.
Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
- 8. Definite Integrals3h 25m
3. Techniques of Differentiation
Derivatives of Trig Functions
Problem 3.5.47Briggs - 3rd Edition
Textbook Question
Find the derivative of the following functions.
y = cot x / (1 + csc x)

1
Step 1: Identify the functions involved. The given function is . This is a quotient of two functions: the numerator and the denominator .
Step 2: Apply the Quotient Rule for derivatives. The Quotient Rule states that if , then .
Step 3: Find the derivative of the numerator . The derivative .
Step 4: Find the derivative of the denominator . The derivative .
Step 5: Substitute , , , and into the Quotient Rule formula: . Simplify the expression to find the derivative.
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