Question

Найдите производную функций 1) f(x)=3x^8 2) f(x)=-1/9x^-9 ПОЖАЛУЙСТА ♥️♥️♥️

Answer 1

1) f(x)=3x^8
     f'(x) = 24x^7
2) f(x)=-1/9x^-9 = -1/9*x^9
    f'(x) = -x^8

Answer 2

Derivative of f(x) = 3x^8

To find the derivative of the function f(x) = 3x^8, we can use the power rule of differentiation. According to the power rule, if we have a function of the form f(x) = ax^n, where a is a constant and n is a real number, the derivative is given by:

f'(x) = n * ax^(n-1)

Applying the power rule to the function f(x) = 3x^8, we get:

f'(x) = 8 * 3x^(8-1) = 24x^7

Therefore, the derivative of f(x) = 3x^8 is f'(x) = 24x^7.

Derivative of f(x) = -1/9x^-9

To find the derivative of the function f(x) = -1/9x^-9, we can again use the power rule of differentiation. However, we need to be careful with the negative exponent.

First, let's rewrite the function as f(x) = -1/(9x^9). Now, applying the power rule, we have:

f'(x) = -1 * (9x^9)^(-1-1) * 9 = -9x^(-10) * 9 = -81x^(-10)

Therefore, the derivative of f(x) = -1/9x^-9 is f'(x) = -81x^(-10).

I hope this helps! Let me know if you have any further questions.