Question

F(x)=x²+4x-7. f'(x)=​

Answer 1

Ответ: 2x + 4.

Подробное нахождение производной через формулы снизу на фотографии:

Answer 2

To find the derivative of the function $f(x) = x^2 + 4x - 7$ with respect to $x$, we'll apply the rules of differentiation. The power rule and the sum rule will be used in this case.

The power rule states that if you have a term $ax^n$, the derivative is $anx^{n-1}$. And the sum rule states that the derivative of a sum of functions is the sum of the derivatives of those functions.

Let's differentiate each term separately:

1. $\frac{d}{dx}(x^2) = 2x^{2-1} = 2x$
2. $\frac{d}{dx}(4x) = 4$
3. $\frac{d}{dx}(-7) = 0$

Now, combining these results using the sum rule:

$f'(x) = \frac{d}{dx}(x^2) + \frac{d}{dx}(4x) + \frac{d}{dx}(-7) = 2x + 4 + 0 = 2x + 4$

So, the derivative of $f(x) = x^2 + 4x - 7$ with respect to $x$ is $f'(x) = 2x + 4$.