Question

ПОМОГИТЕ СРОЧНО ПРОШУ 1) Найдите производную функции у = e3x-2. в точке х=2/3 2) Найдите производную функции у = е2х+3 в точке х=-1,5 3) Найдите значение производной функции у = е5 - 3х в точке 1 ДАЮ 50 БАЛЛОВ, ОТВЕТЬТЕ НА ВСЕ 3 ПОЖАЛУЙСТА

Answer 1

Ответ:

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Объяснение:

Answer 2

Derivative of the Function y = e^(3x-2) at x = 2/3:

To find the derivative of the function y = e^(3x-2) at x = 2/3, we can use the chain rule. The chain rule states that if we have a composite function, such as f(g(x)), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).

In this case, the outer function is e^x, and the inner function is 3x-2. Let's find the derivative step by step:

1. Find the derivative of the outer function e^x, which is e^x itself. 2. Find the derivative of the inner function 3x-2, which is 3. 3. Multiply the derivatives from steps 1 and 2 together to get the derivative of the composite function.

Therefore, the derivative of y = e^(3x-2) is given by:

dy/dx = e^(3x-2) * 3

Now, let's substitute x = 2/3 into the derivative expression to find the value of the derivative at x = 2/3:

dy/dx = e^(3(2/3)-2) * 3 = e^0 * 3 = 3

So, the derivative of the function y = e^(3x-2) at x = 2/3 is 3.

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