Question

Производная функции 2/(x(квадрат) - 4 )в квадрате . спасибо

Answer 1

Derivative of the Function 2/(x^2 - 4)^2

To find the derivative of the function 2/(x^2 - 4)^2, we can use the chain rule. Let's break down the steps:

1. Rewrite the function: The given function can be rewritten as 2 * (x^2 - 4)^(-2).

2. Apply the chain rule: The chain rule states that if we have a composite function f(g(x)), then the derivative is given by f'(g(x)) * g'(x). In this case, the outer function is 2 * u^(-2), where u = (x^2 - 4), and the inner function is u = (x^2 - 4).

3. Find the derivative of the outer function: The derivative of 2 * u^(-2) with respect to u is -4 * u^(-3).

4. Find the derivative of the inner function: The derivative of u = (x^2 - 4) with respect to x is 2x.

5. Combine the derivatives: Multiplying the derivative of the outer function (-4 * u^(-3)) with the derivative of the inner function (2x), we get the derivative of the composite function.

Therefore, the derivative of the function 2/(x^2 - 4)^2 is -8x/(x^2 - 4)^3.

Please note that the above explanation is based on mathematical principles and does not cite specific sources.