Question

Помогите еще 2примера. Производная функции. 3sinX +ctgx. Второй: y=6tgx-cosx Пожалуйста...

Answer 1

1) y=3*sin(x)+ctg(x)
y'=3*cos(x)- (1/sin^(2)*(x))

2) y=6tg(x)-cos(x)
y'=6*(1/cos^(2)*(x))+sin(x)

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Answer 2

Derivative of the function 3sin(x) + ctgx:

To find the derivative of the function 3sin(x) + ctgx, we can use the rules of differentiation.

The derivative of the sum of two functions is equal to the sum of their derivatives. Therefore, we can find the derivative of each term separately and then add them together.

Let's start with the first term, 3sin(x). The derivative of sin(x) is cos(x), so the derivative of 3sin(x) is 3cos(x).

Now let's move on to the second term, ctgx. The derivative of ctgx can be found using the chain rule. The chain rule states that if we have a composite function, f(g(x)), then the derivative is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In this case, the outer function is ctg(x) and the inner function is x. The derivative of ctg(x) is -csc^2(x), and the derivative of x is 1. Therefore, the derivative of ct