Question

Y=ctg(5x+7) найти походную

Answer 1

Вот держи ответ с подробным объяснением

Answer 2

To find the derivative of the given function $Y = \cot(5x + 7)$ with respect to $x$, we'll use the chain rule. The chain rule states that if we have a composition of functions $f(g(x))$, then the derivative with respect to $x$ is $f'(g(x)) \cdot g'(x)$.

The derivative of the cotangent function is defined as:

$\frac{d}{dx} \cot(x) = -\frac{1}{\sin^2(x)}$

Now, let's apply the chain rule to find the derivative of $Y$ with respect to $x$:

$\frac{dY}{dx} = \frac{d}{dx} \cot(5x + 7)$

Using the chain rule:

$\frac{d}{dx} \cot(5x + 7) = -\frac{1}{\sin^2(5x + 7)} \cdot \frac{d}{dx} (5x + 7)$

The derivative of $5x + 7$ with respect to $x$ is simply $5$, as the derivative of a constant term (7) is 0, and the derivative of $5x$ is $5$.

Now, we have:

$\frac{dY}{dx} = -\frac{5}{\sin^2(5x + 7)}$

That's the derivative of $Y$ with respect to $x$.