SUMMARY
The first derivative of the function (1 + tan(x)) is calculated using the quotient rule, resulting in sec^2(x). The derivative of the constant 1 is 0, while the derivative of tan(x) is sec^2(x). This identity simplifies the differentiation process, making it easier for students to handle similar problems in calculus.
PREREQUISITES
- Understanding of basic calculus concepts, specifically derivatives.
- Familiarity with the quotient rule for differentiation.
- Knowledge of trigonometric functions, particularly tangent and secant.
- Ability to manipulate mathematical identities and expressions.
NEXT STEPS
- Study the quotient rule in detail to apply it to more complex functions.
- Learn about the derivatives of other trigonometric functions, such as cotangent and cosecant.
- Explore the application of derivatives in real-world problems, particularly in physics and engineering.
- Practice solving derivative problems involving composite functions and implicit differentiation.
USEFUL FOR
Students studying calculus, mathematics educators, and anyone looking to strengthen their understanding of differentiation techniques and trigonometric identities.
