Question

Найти вторую производную функции: f(x)=x^2-2x^2

Answer 1

F'(x) = 2x-4x;
f''(x) = 2-4 = -2.

памятка : (х^2)' = 2х;
(х)' = 1;

Answer 2

To find the second derivative of the function $f(x) = x^2 - 2x^2$, we'll need to first find its first derivative and then differentiate it again. Let's proceed step by step:

Step 1: Find the first derivative $f'(x)$: To find the first derivative, we'll apply the power rule of differentiation. For a term $x^n$, the derivative is $nx^{n-1}$.

$f(x) = x^2 - 2x^2$

$f'(x) = d/dx [x^2 - 2x^2]$ $f'(x) = 2x^{2-1} - 2(2x)^{2-1}$ $f'(x) = 2x - 2(2x)$ $f'(x) = 2x - 4x$ $f'(x) = -2x$

Step 2: Find the second derivative $f''(x)$: To find the second derivative, we differentiate the first derivative obtained in Step 1.

$f'(x) = -2x$

$f''(x) = d/dx[-2x]$ $f''(x) = -2$

So, the second derivative of the function $f(x) = x^2 - 2x^2$ is $f''(x) = -2$.