Question

Найдите f'(x0), если f(x)=(2-3x)^5 x0=1/3

Answer 1

Ответ: f(x₀)=-15.

Объяснение:

f(x)=(2-3x)⁵    x₀=1/3        f'(x₀)=?

f'(x₀)=((2-3x)⁵)'=5*(2-3x)⁴*(2-3x)'=5*(2-3x)⁴*(-3)=-15*(2-3x)⁴.

f'(1/3)=-15*(2-3*(1/3))⁴=-15*(2-1)⁴=-15*1⁴=-15.

Answer 2

Ответ:

5

Объяснение:

$f(x)=(2-3x)^5\\x_0=\frac{1}{3} \\f(x_0)=(2-3*\frac{1}{3})^5=(2-1)^5=1^5=5$

Answer 3

To find the derivative of the function f(x) at x = x0, we'll first calculate the derivative of the function and then substitute x0 into the result. Let's begin:

Given function: f(x) = (2 - 3x)^5 We need to find f'(x) (the derivative of f(x)).

To find the derivative of (2 - 3x)^5, we can use the chain rule:

Chain rule states that if we have a composite function u(v(x)), then the derivative of u(v(x)) with respect to x is given by u'(v(x)) * v'(x).

In our case: u(v) = v^5, where v = 2 - 3x.

Step 1: Find du/dv: du/dv = d/dv (v^5) = 5v^4

Step 2: Find dv/dx: dv/dx = d/dx (2 - 3x) = -3

Step 3: Find f'(x) using the chain rule: f'(x) = du/dv * dv/dx = 5(2 - 3x)^4 * (-3)

Now, we need to evaluate the derivative at x = x0, which is x0 = 1/3:

f'(1/3) = 5(2 - 3(1/3))^4 * (-3) = 5(2 - 1)^4 * (-3) = 5(1)^4 * (-3) = 5 * (-3) = -15

Therefore, f'(x0) when x0 = 1/3 is -15.