Question

Помогите пожалуйста.Найти производную функции:

Answer 1

1. $y = (5x + {3x}^{3})* {x}^{3 } =5x^4+3x^6$
$y' = 5*4x^3+3*6x^5=20x^3+18x^5$

2. $y = {5x}^{4} - {3x}^{5} + {6x}^{7} + {5x}$
$y' = 5*4x^3-3*5x^4+6*7x^6+5=20x^3-15x^4+42x^6+5$

3. $y = 3 \sqrt{x} + \sqrt{x} + 2 \sqrt{x} + 5 \sqrt{x} =11 \sqrt{x}$
$y'= \frac{11}{2 \sqrt{x} }$

Answer 2

Finding the Derivative of a Function

To find the derivative of a function, we need to differentiate the given function with respect to the variable. Let's consider the functions provided and find their derivatives.

1. Function: f(x) = x-3 - The derivative of the function f(x) = x-3 is 1. - Source: 2. Function: y=(1/3)*x^3-2x^2 - The derivative of the function y=(1/3)*x^3-2x^2 is y' = x^2 - 4x. - Source: 3. Function: y=1-2x - The derivative of the function y=1-2x is y' = -2. - Source: 4. Function: sin^3(x) - The derivative of the function sin^3(x) is 3*sin^2(x)*cos(x). - Source: 5. Function: f(x) = 1 / (1 + e^(-x)) - The derivative of the function f(x) = 1 / (1 + e^(-x)) is f(x)' = f(x) * (1 - f(x)). - Source: 6. Function: O1 = (1 - 0.33) * ((1 - 0.33) * 0.33) - The derivative of the function O1 = (1 - 0.33) * ((1 - 0.33) * 0.33) is not explicitly provided in the search results.

If you have any more functions for which you need the derivatives, feel free to ask!