Question

Найти производную.

Answer 1

У'=(5х^3)'-(sinx)'=5•(x^3)'- cosx=5•3x^2-cosx=
15x^2-cosx

Answer 2

Finding the Derivative

To find the derivative of a function, we need to apply the appropriate rules of differentiation. Let's consider a few examples:

1. Example 1: y = (7 - 24x)^10

To find the derivative of this function, we can use the chain rule. The chain rule states that if we have a composition of functions, the derivative is the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is raising to the power of 10, and the inner function is 7 - 24x. Applying the chain rule, we get:

y' = 10(7 - 24x)^9 * (-24) 2. Example 2: y = sin(ln(x)) * cos(ln(x))

To find the derivative of this function, we can use the product rule. The product rule states that the derivative of the product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function.

In this case, the first function is sin(ln(x)) and the second function is cos(ln(x)). Applying the product rule, we get:

y' = cos(ln(x)) * (ln(x))' * cos(ln(x)) + sin(ln(x)) * (-sin(ln(x))) * (ln(x))' Simplifying further, we get:

y' = 1/x * cos(2ln(x)) 3. Example 3: y = 5x^4 - 20x^3 + 4/x + 9

To find the derivative of this function, we can use the power rule and the sum rule. The power rule states that the derivative of x^n is n*x^(n-1), and the sum rule states that the derivative of the sum of two functions is the sum of their derivatives.

In this case, we have multiple terms, each with a different power of x. Applying the power rule and the sum rule, we get:

y' = 20x^3 - 60x^2 - 4/x^2 These are just a few examples of finding derivatives. Different functions may require different rules and techniques to find their derivatives. If you have a specific function in mind, please let me know and I'll be happy to help you find its derivative.