Question

F(x)=cosx*ln(4-5x) f'(x) - ?

Answer 1

Ответ:1

Пошаговое объяснение:

Answer 2

To find the derivative of the function F(x) = cos(x) * ln(4 - 5x), we'll use the product rule of differentiation. The product rule states that if you have a function of the form u(x) * v(x), then its derivative is given by:

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

where u'(x) represents the derivative of u(x) with respect to x, and v'(x) represents the derivative of v(x) with respect to x.

Let's apply the product rule to F(x):

Let u(x) = cos(x) and v(x) = ln(4 - 5x).

Then, u'(x) = -sin(x) (derivative of cos(x)) and v'(x) = d/dx[ln(4 - 5x)].

Now, let's find v'(x):

Using the chain rule, the derivative of ln(4 - 5x) is 1 / (4 - 5x) multiplied by the derivative of the inner function (4 - 5x) with respect to x:

v'(x) = (1 / (4 - 5x)) * d/dx[4 - 5x] = (1 / (4 - 5x)) * (-5) = -5 / (4 - 5x).

Now, applying the product rule:

F'(x) = u'(x) * v(x) + u(x) * v'(x) F'(x) = (-sin(x)) * ln(4 - 5x) + cos(x) * (-5 / (4 - 5x)) F'(x) = -sin(x) * ln(4 - 5x) - 5cos(x) / (4 - 5x)

So, the derivative of F(x) is F'(x) = -sin(x) * ln(4 - 5x) - 5cos(x) / (4 - 5x).