Question

F(x)=(3x-2)^5 найдите f’(1)

Answer 1

Ответ:

Пошаговое объяснение:

f'(x)= 5*3(3x-2)⁴

f'(x)=15(3-2)⁴= 15*1= 15

Answer 2

To find the value of the derivative of the function F(x) = (3x - 2)^5 at x = 1, we need to compute the derivative of F(x) and then evaluate it at x = 1.

The derivative of a function in the form (a * u)^n with respect to x is given by:

d/dx [(a * u)^n] = n * a^(n-1) * u^(n-1) * du/dx

where u is the inner function (in this case, 3x - 2), and du/dx is the derivative of u with respect to x.

For our function F(x) = (3x - 2)^5:

u = 3x - 2 n = 5

Now, let's find the derivative of F(x):

F'(x) = 5 * (3x - 2)^(5-1) * (d/dx [3x - 2])

The derivative of (3x - 2) with respect to x is just 3, as the derivative of a constant (in this case, -2) is zero.

F'(x) = 5 * (3x - 2)^4 * 3

Now, let's find the value of f'(1) by substituting x = 1 into the derivative expression:

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

So, the value of the derivative of F(x) = (3x - 2)^5 at x = 1 is 15.