Question

Найти производную функции: f(x)=(9x-13)^9

Answer 1

Ответ:

81(9x-13)⁸

Пошаговое объяснение:

f'(x) = ((9x-13)⁹)' = 9(9x-13)⁸ * (9x-13)' =  9(9x-13)⁸ * 9 = 81(9x-13)⁸

Answer 2

To find the derivative of the function $f(x) = (9x - 13)^9$, we can use the chain rule. The chain rule states that if we have a function of the form $g(h(x))$, then its derivative with respect to $x$ is given by $g'(h(x)) \cdot h'(x)$. Let's apply this rule step by step:

Step 1: Identify the outer function $g(u) = u^9$, where $u = 9x - 13$. Step 2: Find the derivative of the outer function: $g'(u) = 9u^{9-1} = 9u^8$. Step 3: Identify the inner function $h(x) = 9x - 13$. Step 4: Find the derivative of the inner function: $h'(x) = 9$.

Now, we can apply the chain rule:

$f'(x) = g'(h(x)) \cdot h'(x) = 9(9x - 13)^8 \cdot 9 = 81(9x - 13)^8.$

So, the derivative of the function $f(x) = (9x - 13)^9$ is $f'(x) = 81(9x - 13)^8$.