Question

Найти производную функции y=ctg(6x-1)

Answer 1

Y(x) = ctg(6x-1)
y ` (x) = - 6 / sin^2(6x-1)

Сначала находим производную от внешней функции
( ctg(6x-1) )` = - 1 / sin^2(6x-1) ,
затем домножаем на производную от внутренней
(6x-1)` = 6

Answer 2

Derivative of y=ctg(6x-1)

To find the derivative of the function y=ctg(6x-1), we can use the chain rule for differentiation. The derivative of the cotangent function is -csc^2(x), and the derivative of the inner function (6x-1) is 6. Therefore, the derivative of y with respect to x is:

y' = -csc^2(6x-1) * 6

Let's cite the relevant search snippets to confirm this result.

: "y = ctg x => y' = -1/sin^2x"

Based on the above snippet, the derivative of cotangent function is -1/sin^2x.

: "y = Cf(x) => y' = C.f'(x)"

This snippet provides the general rule for finding the derivative of a function composed with another function.

Therefore, the derivative of the given function y=ctg(6x-1) is y' = -6*csc^2(6x-1).