Question

Найти производную: (2х-3)^3

Answer 1

Ответ:

$\frac{dx}{x} (2x - 3)^{3} = 3(2x - 3)^{2} ×2= 24x^{2} - 72x + 54$

Answer 2

To find the derivative of the function $f(x) = (2x - 3)^3$ with respect to $x$, we can use the chain rule.

The chain rule states that if we have a composition of functions $u(x)$ and $v(x)$, i.e., $f(x) = u(v(x))$, then the derivative of $f(x)$ with respect to $x$ is given by $\frac{{df}}{{dx}} = \frac{{du}}{{dv}} \cdot \frac{{dv}}{{dx}}$.

In our case, $u(v) = v^3$ and $v(x) = 2x - 3$. Let's find the derivatives:

Step 1: Find $\frac{{du}}{{dv}}$ $u(v) = v^3$ $\frac{{du}}{{dv}} = 3v^2$

Step 2: Find $\frac{{dv}}{{dx}}$ $v(x) = 2x - 3$ $\frac{{dv}}{{dx}} = 2$

Step 3: Apply the chain rule formula to get $\frac{{df}}{{dx}}$ $\frac{{df}}{{dx}} = \frac{{du}}{{dv}} \cdot \frac{{dv}}{{dx}} = 3(2x - 3)^2 \cdot 2$

Therefore, the derivative of $f(x) = (2x - 3)^3$ with respect to $x$ is $\frac{{df}}{{dx}} = 6(2x - 3)^2$.