Question

Найти производную функции

Answer 1

F(x) = 3Sin(x/3 - π/2) = -3Sin(π/2 - x/3) = -3Cosx/3
f'(x) =3Sinx/3 * (x/3)' = 3Sinx/3 * 1/3= Sinx/3

Answer 2

Finding the Derivative of a Function

To find the derivative of a function, we need to differentiate it with respect to the independent variable. Here are a few examples of finding the derivative of different functions:

1. Example 1: - Function: \(y = 9x\) - Derivative: \(y' = 9\) 2. Example 2: - Function: \(y = 5x^4 - 20x\) - Derivative: \(y' = 20x^3 - 20\) 3. Example 3: - Function: \(y = (7 - 24x)^{10}\) - Derivative: \(y' = -240(7 - 24x)^9\) 4. Example 4: - Function 1: \(y = 8x + \sin(x) + 5\) - Derivative 1: \(y' = 8 + \cos(x)\) - Function 2: \(y = 2 + \cos(x) + 3x + 5\) - Derivative 2: \(y' = -\sin(x) + 3\) 5. Example 5: - Function: \(y = \sin(x)\) - Derivative: \(y' = \cos(x)\) - Function: \(y = \cos(x)\) - Derivative: \(y' = -\sin(x)\) 6. Example 6: - Function: \(y = -\frac{1}{3}(4 + 3x)^6\) - Derivative: \(y' = -2(4 + 3x)^5\) 7. Example 7: - Function: \(y = \sin(\ln(x)) \cdot \cos(\ln(x))\) - Derivative: \(y' = \frac{1}{x} \cdot \cos^2(\ln(x)) - \sin^2(\ln(x)) = \frac{\cos(2\ln(x))}{x}\) [[8]](https://uchi.ru/otvety/questions/nayti-proizvodnuyu-podrobno-y-sin-lnx-cos-lnx)

8. Example 8: - Function: \(y = 8x^3 + 3x^2 - x\) - Derivative: \(y' = 24x^2 + 6x - 1\) Please note that these are just a few examples, and there are many more functions and rules for finding derivatives. Let me know if you have any specific function you would like me to find the derivative of.