Question

ctg3x/√x Помогите найти производную.

Answer 1

Решение во вложения, удачи.

Answer 2

Finding the Derivative of ctg(3x)/√x

To find the derivative of the given function ctg(3x)/√x, we can use the quotient rule, which states that if we have a function in the form of u/v, then the derivative is (v*u' - u*v') / v^2, where u' and v' are the derivatives of u and v, respectively.

Applying the quotient rule to the given function, we get:

y = ctg(3x)/√x

Now, let's find the derivative of y with respect to x.

The derivative of ctg(3x) is -3*ctg(3x)^2*csc(3x) The derivative of √x is 1/(2*√x).

Using the quotient rule, the derivative of the given function is: y' = (-√x*3*ctg(3x)^2*csc(3x) - ctg(3x)/(2*√x^2))

Therefore, the derivative of ctg(3x)/√x is y' = (-3*ctg(3x)^2*csc(3x)*√x - ctg(3x)/(2*√x^3)).