Question

Помогите с решением производной y=ctg(2xsin1/2) можно не полнстью решение,хотя бы путь решения..

Answer 1

Самый простой путь. по формуле y'=(ctgu)' = -1/sin^2u * u'

Answer 2

Finding the Derivative of y=ctg(2xsin(1/2))

To find the derivative of y=ctg(2xsin(1/2)), we can use the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

Solution:

The derivative of the cotangent function is -csc^2(x), and the derivative of the inner function 2xsin(1/2) is 2cos(1/2).

Therefore, the derivative of y=ctg(2xsin(1/2)) is:

y' = -csc^2(2xsin(1/2)) * 2cos(1/2)

Let's break it down: - The derivative of the cotangent function is -csc^2(x). - The derivative of the inner function 2xsin(1/2) is 2cos(1/2).

So, the derivative of y=ctg(2xsin(1/2)) is y' = -csc^2(2xsin(1/2)) * 2cos(1/2).

This is the general approach to finding the derivative of y=ctg(2xsin(1/2)). If you need further assistance or a more detailed explanation, feel free to ask!