Question

Y=x^4-x^2+1найти производную функции

Answer 1

Ответ: у' = 4х^3 - 2х

Answer 2

To find the derivative of the given function $y = x^4 - x^2 + 1$, we can use the rules of differentiation.

The power rule states that if we have a term of the form $x^n$, the derivative with respect to $x$ is given by $nx^{(n-1)}$.

Applying the power rule to each term, we get:

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

Now, the derivatives of $x^4$, $x^2$, and $1$ with respect to $x$ are:

$\frac{d}{dx}(x^4) = 4x^{4-1} = 4x^3$

$\frac{d}{dx}(x^2) = 2x^{2-1} = 2x$

$\frac{d}{dx}(1) = 0$ (the derivative of a constant is always zero)

Putting it all together:

$\frac{dy}{dx} = 4x^3 - 2x + 0$

So, the derivative of the function $y = x^4 - x^2 + 1$ is $4x^3 - 2x$.