Question

Продифференцировать данные функции: y=ln((1-e^x)/(e^x))

Answer 1

Готово.....................

Answer 2

Differentiating the Function

To differentiate the given function y = ln((1 - e^x)/(e^x)), we can use the chain rule and the quotient rule of differentiation.

Let's break down the steps:

1. Apply the quotient rule: The quotient rule states that if we have a function of the form f(x) = g(x)/h(x), then the derivative of f(x) is given by (g'(x) * h(x) - g(x) * h'(x))/(h(x))^2.

2. Identify the numerator and denominator of the function: - Numerator: (1 - e^x) - Denominator: e^x

3. Differentiate the numerator and denominator separately: - Derivative of the numerator: (d/dx)(1 - e^x) = 0 - (d/dx)(e^x) = -e^x - Derivative of the denominator: (d/dx)(e^x) = e^x

4. Apply the quotient rule: - (g'(x) * h(x) - g(x) * h'(x))/(h(x))^2 = (-e^x * e^x - (1 - e^x) * e^x)/(e^x)^2

5. Simplify the expression: - (-e^2x - e^x + e^2x)/(e^2x) = -e^x/(e^2x) - 1/(e^x) + 1/(e^2x)

Therefore, the derivative of the function y = ln((1 - e^x)/(e^x)) is -e^x/(e^2x) - 1/(e^x) + 1/(e^2x).

Please note that the above differentiation steps are based on the provided function and the rules of differentiation.