Question

Производная F(x) = x^3/3-7x^4

Answer 1

$f'(x)=(\frac{x^3}{3} -7x^4)'=3\frac{x^2}{3} -7*4x^3=x^2-28x^3$

Answer 2

Ответ:

Пошаговое объяснение:

F'(x)=3x^2/3-28x^3=x^2-28x^3

Answer 3

To find the derivative of the given function $F(x) = \frac{x^3}{3} - 7x^4$, we'll use the basic rules of differentiation. The general power rule states that if $f(x) = x^n$, then the derivative of $f(x)$ with respect to $x$ is $f'(x) = n \cdot x^{n-1}$.

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

Step 1: Differentiate $\frac{x^3}{3}$: Using the power rule, the derivative of $\frac{x^3}{3}$ with respect to $x$ is: $\frac{d}{dx}\left(\frac{x^3}{3}\right) = \frac{1}{3} \cdot 3x^{3-1} = x^2$.

Step 2: Differentiate $-7x^4$: Using the power rule, the derivative of $-7x^4$ with respect to $x$ is: $\frac{d}{dx}(-7x^4) = -7 \cdot 4x^{4-1} = -28x^3$.

Step 3: Combine the derivatives: Now, since the function $F(x)$ is the sum of $\frac{x^3}{3}$ and $-7x^4$, we can simply add their derivatives: $F'(x) = x^2 - 28x^3$.

So, the derivative of the function $F(x) = \frac{x^3}{3} - 7x^4$ with respect to $x$ is $F'(x) = x^2 - 28x^3$.