Question

помогите найти производную функций: 1) у=х в 8 степени 2) у= корень 4 степени из х в 5 степени

Answer 1

1. y'=8x в 7 степени

2. y'=5/4 x в степени -1/4=5/ 4*корень четвертой степени из х

Answer 2

1)у=х⁸, производная =8х⁷

2)у=х в степени 5/4, производная=5/4*х в степени1/4 или 5/4*корень 4 степени х

Answer 3

Finding Derivatives of Functions

To find the derivative of the given functions, we can use the rules of differentiation. Let's calculate the derivatives for the given functions:

1. Function: y = x^8 2. Function: y = (x^4)^(1/5)

Derivative of y = x^8

The derivative of the function y = x^8 can be found using the power rule of differentiation, which states that the derivative of x^n is n*x^(n-1).

The derivative of y = x^8 is: y' = 8x^7

Derivative of y = (x^4)^(1/5)

The derivative of the function y = (x^4)^(1/5) can be found using the chain rule of differentiation, which states that the derivative of f(g(x)) is f'(g(x)) * g'(x).

Let's calculate the derivative step by step: 1. Let u = x^4 2. Then y = u^(1/5)

Using the chain rule, the derivative of y = (x^4)^(1/5) is: y' = (1/5) * (x^4)^(-4/5) * 4x^3 y' = (4/5) * x^3 * (x^4)^(-4/5) y' = (4/5) * x^3 * (x^(-4)) y' = (4/5) * x^(-1) y' = 4/5x

So, the derivative of y = (x^4)^(1/5) is: y' = 4/5x Therefore, the derivatives of the given functions are: 1. For y = x^8, the derivative is y' = 8x^7. 2. For y = (x^4)^(1/5), the derivative is y' = 4/5x.