Question

Производная функции у=(3х+1)^3 имеет вид: А) у=(3х+1)^2 Б) у=3(3х+1)^2 В)у=9(3х+1)^2 Г)у=9

Answer 1

Б Y=3(3x+1)^2.........

Answer 2

To find the derivative of the function $y = (3x + 1)^3$ with respect to $x$, we can use the chain rule of differentiation.

The chain rule states that if we have a composite function $y = u^n$, where $u$ is a differentiable function of $x$ and $n$ is a constant, then the derivative of $y$ with respect to $x$ is given by:

$\frac{dy}{dx} = n \cdot u^{n-1} \cdot \frac{du}{dx}$

In this case, $u = 3x + 1$ and $n = 3$. Now, let's find the derivative:

$\frac{dy}{dx} = 3 \cdot (3x + 1)^{3-1} \cdot \frac{d}{dx}(3x + 1)$

The derivative of $3x + 1$ with respect to $x$ is simply 3, as the derivative of a constant term (1 in this case) is 0, and the derivative of $3x$ is 3.

$\frac{dy}{dx} = 3 \cdot (3x + 1)^2 \cdot 3$

Simplifying further:

$\frac{dy}{dx} = 9 \cdot (3x + 1)^2$

So, the correct answer is $\mathbf{В) у = 9(3x + 1)^2}$.