Question

Найти производную функций

Answer 1

Чего?! я ниче не поняла:)

Answer 2

Finding Derivatives of Functions

To find the derivative of a function, we need to determine how the function changes with respect to its independent variable. Here are a few examples of finding derivatives of different functions:

1. Example 1: - Function: y = 9 + 2x - Derivative: y' = 2 - Explanation: The derivative of a constant term is zero, and the derivative of 2x is 2. Therefore, the derivative of y = 9 + 2x is y' = 2.

2. Example 2: - Function: y = (7 - 24x)^10 - Derivative: y' = -240 * (7 - 24x)^9 - Explanation: To find the derivative of a function raised to a power, we use the chain rule. The derivative of (7 - 24x) is -24, and the derivative of (7 - 24x)^9 is 9 * (7 - 24x)^8. Multiplying these two derivatives gives us y' = -240 * (7 - 24x)^9.

3. Example 3: - Function: f(x) = sin(x) - Derivative: f'(x) = cos(x) - Explanation: The derivative of the sine function is the cosine function. Therefore, the derivative of f(x) = sin(x) is f'(x) = cos(x).

4. Example 4: - Function: g(x) = cos(x) - Derivative: g'(x) = -sin(x) - Explanation: The derivative of the cosine function is the negative sine function. Therefore, the derivative of g(x) = cos(x) is g'(x) = -sin(x).

5. Example 5: - Function: y(x) = x - y + arctan(y) = 0 - Derivative: y'(x) = 1 - y'(x) + 1/(1 + y^2) * y'(x) - Explanation: To find the derivative of an implicit function, we use the implicit differentiation method. In this case, we differentiate each term with respect to x and treat y as a function of x. The derivative of x with respect to x is 1, the derivative of -y with respect to x is -y'(x), and the derivative of arctan(y) with respect to x is 1/(1 + y^2) * y'(x). Simplifying the equation gives us y'(x) = 1 - y'(x) + 1/(1 + y^2) * y'(x).

These are just a few examples of finding derivatives of different functions. The process may vary depending on the specific function and rules of differentiation.