Question

F(x)=x²/2-5/x²+4 f'(x)=?

Answer 1

виу виу виу,помощь тута

Answer 2

To find the derivative of the function $f(x) = \frac{x^2}{2} - \frac{5}{x^2} + 4$, you can use the power rule for differentiation. The power rule states that if you have a term of the form $ax^n$, where $a$ and $n$ are constants, the derivative is $anx^{n-1}$.

Let's find the derivative of each term in your function $f(x)$:

1. The derivative of $\frac{x^2}{2}$ with respect to $x$ is $\frac{1}{2} \cdot 2x = x$.

2. The derivative of $-\frac{5}{x^2}$ can be calculated using the power rule for negative exponents. The term $-\frac{5}{x^2}$ can be rewritten as $-5x^{-2}$. The derivative is $2 \cdot 5x^{-2-1} = -10x^{-3}$.

3. The derivative of the constant term 4 is 0 since the derivative of a constant is always 0.

Now, add up the derivatives of each term to find the derivative of the entire function:

$f'(x) = x - 10x^{-3} + 0$

Simplify this expression:

$f'(x) = x - \frac{10}{x^3}$

So, the derivative of the function $f(x)$ is $f'(x) = x - \frac{10}{x^3}$.