Question

F(3x+5)=6x-1 ,найдите f'(x)​

Answer 1

Ответ:

f'(x) = 2

Пошаговое объяснение:

Попробуем формулу привести к виду f(x)

Пусть y = 3x + 5. Тогда обратная функция будет равна y = (x - 5)/3

Подставляем эту функцию как аргумент в исходную функцию, и получаем

$f(x) = \frac{6(x-5)}{3} - 1 = 2x - 11$

Теперь задача становится элементарной, и f'(x) = 2

Answer 2

To find the derivative of the function f(x) with respect to x, we'll use the chain rule. The chain rule states that if we have a composite function F(g(x)), then the derivative of F with respect to x is given by F'(g(x)) * g'(x).

Let's find the derivative of the given function F(3x + 5) with respect to x:

F(3x + 5) = 6x - 1

To apply the chain rule, we'll treat 3x + 5 as the inside function g(x). The outside function F(u) is 6u - 1, where u = 3x + 5.

Now, we find the derivative of the outside function F(u) with respect to u:

F'(u) = d/dx (6u - 1) = 6

Next, we find the derivative of the inside function g(x) with respect to x:

g(x) = 3x + 5 g'(x) = d/dx (3x + 5) = 3

Finally, applying the chain rule, we get:

f'(x) = F'(g(x)) * g'(x) f'(x) = 6 * 3 f'(x) = 18

So, the derivative of f(x) with respect to x is 18.