Question

Найти значение производной в точке x=1, f(x)=1/x^4

Answer 1

Запишем функцию в виде f(x)=x^(-4), тогда её производная f'(x)=-4*x^(-5)=-4/x^5. При этом f'(1)=-4. Ответ: -4.

Answer 2

f(x)= x^-4

f'(x)+ -4x^-5 = -4/x^5

f'(1) = -4/1^5 = -4/1=-4

Answer 3

To find the derivative of the function $f(x) = \frac{1}{x^4}$ and evaluate it at $x = 1$, we'll use the rules of differentiation. The derivative of $f(x)$ with respect to $x$ is denoted by $f'(x)$ and can be found using the power rule:

$\frac{d}{dx}\left(\frac{1}{x^n}\right) = -\frac{n}{x^{n+1}}$

where $n$ is a constant. In our case, $n = 4$.

Step 1: Find the derivative $f'(x)$: $f'(x) = -\frac{4}{x^{4+1}} = -\frac{4}{x^5}$

Step 2: Evaluate the derivative at $x = 1$: $f'(1) = -\frac{4}{1^5} = -4$

So, the value of the derivative at $x = 1$ is $-4$.