Question

Производная функции y=sin(5-2x) имеет вид: 1) y=-2cos(5-2x) 2)y=-2sin(5-2x) 3)y=cos(5-2x) 4)y=2 cos(5-2x)

Answer 1

Решение задания смотри на фотографии

Answer 2

To find the derivative of the function $y = \sin(5-2x)$ 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 its derivative is given by $f'(g(x)) \cdot g'(x)$.

In this case, $g(x) = 5 - 2x$ and $f(u) = \sin(u)$, where $u = g(x)$. The derivative of $f(u) = \sin(u)$ with respect to $u$ is $\cos(u)$, and the derivative of $g(x) = 5 - 2x$ with respect to $x$ is $-2$.

Now, we apply the chain rule:

$\frac{dy}{dx} = f'(g(x)) \cdot g'(x) = \cos(5-2x) \cdot (-2) = -2\cos(5-2x)$

So, the correct option is: 1) $y = -2\cos(5-2x)$.