Question

Найдите f’(x) если f’(x)=(3x-5)(7-x)

Answer 1

$f(x) = (3x - 5)(7 - x) \\ f'(x) = (3x - 5)'(7 - x) + (7 - x)'(3x - 5) = \\ 3(7 - x) - (3x - 5) = 21 - 3x - 3x + 5 = \\ 26 - 6x$

Answer 2

To find the derivative of f(x), we can use the product rule, which states that if we have two functions u(x) and v(x), then the derivative of their product is given by:

(d/dx)(u(x) * v(x)) = u'(x) * v(x) + u(x) * v'(x)

In this case, u(x) = (3x - 5) and v(x) = (7 - x). Let's find the derivatives of these functions first:

u'(x) = d/dx(3x - 5) = 3 v'(x) = d/dx(7 - x) = -1

Now we can apply the product rule:

f'(x) = (3x - 5) * (-1) + (7 - x) * 3 = -3x + 5 + 21 - 3x = -6x + 26

Therefore, the derivative of f(x) is f'(x) = -6x + 26.