Question

F(x)=x4-2x2+1 дифференциал функции

Answer 1

Ответ:

d(x^4-2x^2+1)'=4x-4x+0=0

Объяснение:

нахождение дифференциала то же самое, что и нахождение производной, по таблице производных

Answer 2

To find the differential of the function $F(x) = x^4 - 2x^2 + 1$, we'll take the derivative with respect to $x$.

The differential of a function $F(x)$ is given by $dF(x) = F'(x) \, dx$, where $F'(x)$ is the derivative of $F(x)$ with respect to $x$ and $dx$ represents the infinitesimal change in $x$.

Let's find the derivative $F'(x)$ first:

$F'(x) = \frac{d}{dx}(x^4 - 2x^2 + 1)$

To differentiate each term, we'll use the power rule:

1. The derivative of $x^4$ with respect to $x$ is $4x^{4-1} = 4x^3$.
2. The derivative of $-2x^2$ with respect to $x$ is $-2 \cdot 2x^{2-1} = -4x$.
3. The derivative of $1$ with respect to $x$ is $0$ (since it's a constant).

Putting it all together:

$F'(x) = 4x^3 - 4x$

Now that we have the derivative, we can write the differential:

$dF(x) = (4x^3 - 4x) \, dx$

This is the differential of the function $F(x) = x^4 - 2x^2 + 1$.