Derivada del Seno | Ejemplo 2

Summary

In this tutorial, the instructor explains how to derive the sine function, including more complex cases with non-simple angles and exponents. The lesson begins with a basic review of sine’s derivative and then moves on to solving problems involving more challenging scenarios. Emphasis is placed on breaking the process into parts: first, deriving the sine, followed by the angle, and then handling the exponent if present. Key tips are provided to avoid common mistakes. The video includes examples for practice, and viewers are encouraged to apply the steps systematically for correct results.

Takeaways

• 😀 The derivative of the sine function is the cosine of the angle. The angle itself is not derived at this step.
• 😀 When differentiating a sine function with an angle other than x, it's essential to differentiate the sine and the angle separately.
• 😀 A common mistake is to try to differentiate both the sine and the angle simultaneously, but the correct approach is to separate these steps.
• 😀 In the first exercise, the derivative of sine with respect to the angle results in cosine, while the derivative of the angle itself is handled separately.
• 😀 For functions where the sine has a power, start by differentiating the exponent first, then the sine, and finally the angle.
• 😀 In the second exercise, the instructor demonstrates how to handle a sine function raised to a power, stressing that this involves three steps: exponent, sine, and angle.
• 😀 When an exponent is involved, first reduce the exponent by 1 after multiplying by the original exponent. This step does not involve the sine or angle yet.
• 😀 Always differentiate the angle independently once the sine and its exponent are already handled.
• 😀 In both exercises, the final result is simplified by multiplying constants, and the expression is reordered for clarity.
• 😀 The instructor emphasizes avoiding shortcuts and recommends writing out all the steps for clarity when differentiating complex functions.