Question

Дано f(x)=3x-2/5x+8 найдите f`(x)

Answer 1

Раскрывать знаменатель не хочется. Ничего красивого не выйдет

Answer 2

     3(5x+8)-5(3x-2)   15x+24-15x+10       34
y'=---------------------=----------------------= -------------
          (5x+8)²               (5x+8)²               (5x+8)²

Answer 3

To find the derivative of the function f(x) = (3x - 2) / (5x + 8), we will use the quotient rule. The quotient rule states that for a function of the form f(x) = u(x) / v(x), the derivative f'(x) is given by:

f'(x) = [v(x) * u'(x) - u(x) * v'(x)] / [v(x)]^2

where u'(x) and v'(x) are the derivatives of u(x) and v(x) with respect to x, respectively.

Let's apply the quotient rule to find the derivative of f(x):

u(x) = 3x - 2 v(x) = 5x + 8

u'(x) = d/dx (3x - 2) = 3 v'(x) = d/dx (5x + 8) = 5

Now, using the quotient rule:

f'(x) = [(5x + 8) * (3) - (3x - 2) * (5)] / [(5x + 8)^2]

Simplifying further:

f'(x) = (15x + 24 - 15x + 10) / (25x^2 + 80x + 64) f'(x) = (34) / (25x^2 + 80x + 64)

So, the derivative of f(x) is f'(x) = 34 / (25x^2 + 80x + 64).