Question

найти производную:

Answer 1

v'(t)=6-0.6t            /////////////////////////////////////////////////////////////////

Answer 2

Немного теории:

 

(u - v)' = u' - v'

(cx)' = c

(u^n) = n · x^(n - 1) · u'

 

V'(t) = (6t - 0,3t²)' = u' - v' = (6t)' - (3t²)' = 6 - 6t

 

Ответ: 6 - 6t

Answer 3

Finding the Derivative

To find the derivative of a function, we need to use the rules of differentiation. Let's consider the function y = sin(ln(x)) * cos(ln(x)).

Using the product rule of differentiation, which states that the derivative of the product of two functions is equal to the derivative of the first function times the second function, plus the first function times the derivative of the second function, we can find the derivative of the given function.

Applying the product rule to the function y = sin(ln(x)) * cos(ln(x)), we have:

y' = (sin(ln(x)))' * cos(ln(x)) + sin(ln(x)) * (cos(ln(x)))'.

Now, let's find the derivatives of the individual functions:

1. Derivative of sin(ln(x)): - Using the chain rule, which states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function, we have: - (sin(ln(x)))' = cos(ln(x)) * (ln(x))' = cos(ln(x)) * (1/x) = cos(ln(x))/x [[3]](https://uchi.ru/otvety/questions/nayti-proizvodnuyu-podrobno-y-sin-lnx-cos-lnx).

2. Derivative of cos(ln(x)): - Using the chain rule again, we have: - (cos(ln(x)))' = -sin(ln(x)) * (ln(x))' = -sin(ln(x)) * (1/x) = -sin(ln(x))/x [[3]](https://uchi.ru/otvety/questions/nayti-proizvodnuyu-podrobno-y-sin-lnx-cos-lnx).

Now, substituting the derivatives back into the original equation, we get:

y' = (cos(ln(x))/x) * cos(ln(x)) + sin(ln(x)) * (-sin(ln(x))/x) [[3]](https://uchi.ru/otvety/questions/nayti-proizvodnuyu-podrobno-y-sin-lnx-cos-lnx).

Simplifying further, we have:

y' = (cos^2(ln(x)) - sin^2(ln(x)))/x = cos(2ln(x))/x [[3]](https://uchi.ru/otvety/questions/nayti-proizvodnuyu-podrobno-y-sin-lnx-cos-lnx).

Therefore, the derivative of the function y = sin(ln(x)) * cos(ln(x)) is y' = cos(2ln(x))/x.

Please let me know if you need any further clarification or assistance!