Question

Y=5x^5-3x³+x+4 Y¹= Плиз срочно

Answer 1

Это производная?
Если да, то
25x^4-9x^2+1

Answer 2

To find the first derivative of the function $Y = 5x^5 - 3x^3 + x + 4$, we need to differentiate it with respect to $x$. The first derivative is denoted as $Y'$ or $\frac{dY}{dx}$.

Let's calculate it step by step:

Step 1: Differentiate $5x^5$ with respect to $x$. The derivative of $x^n$ with respect to $x$ is $n \cdot x^{n-1}$. So, $\frac{d}{dx} (5x^5) = 5 \cdot 5x^{5-1} = 25x^4$.

Step 2: Differentiate $-3x^3$ with respect to $x$. Similar to above, $\frac{d}{dx} (-3x^3) = -3 \cdot 3x^{3-1} = -9x^2$.

Step 3: Differentiate $x$ with respect to $x$. The derivative of $x$ with respect to $x$ is simply 1. So, $\frac{d}{dx}(x) = 1$.

Step 4: Differentiate the constant term $4$ with respect to $x$. The derivative of a constant is always 0. So, $\frac{d}{dx}(4) = 0$.

Now, putting it all together, the first derivative of the function $Y$ is:

$Y' = 25x^4 - 9x^2 + 1$

So, the first derivative of $Y$ with respect to $x$ is $Y' = 25x^4 - 9x^2 + 1$.