Question

Homework 1. f(x) =x^2-2 f'(x) =? 2. f(x) = 3x-1 f'(x) =? 3. f(x) =4x^2+2 f'(x) =? 4. f(x) =7x^2+1 f'(x) =? 5. f(x) = x^2-2 f'(x) =? ​​

Answer 1

Ответ:

Объяснение:

1. f(x) =x^2-2 f'(x) =(x^2-2)'=2x

2. f(x) = 3x-1 f'(x) =(3x-1)'=3

3. f(x) =4x^2+2 f'(x) =(4x^2+2)'=8x

4. f(x) =7x^2+1 f'(x) =(7x^2+1)'=14x

5. f(x) = x^2-2 f'(x) =(x^2-2)'=2x

Answer 2

To find the derivative of a function with respect to x, you can use the power rule, which states that if you have a term of the form ax^n, the derivative is n * ax^(n-1).

Let's find the derivatives of the given functions:

1. f(x) = x^2 - 2 f'(x) = 2x

2. f(x) = 3x - 1 f'(x) = 3

3. f(x) = 4x^2 + 2 f'(x) = 8x

4. f(x) = 7x^2 + 1 f'(x) = 14x

5. It appears that you've repeated the first function: f(x) = x^2 - 2 f'(x) = 2x

So, the derivatives of the functions are as follows:

1. f'(x) = 2x
2. f'(x) = 3
3. f'(x) = 8x
4. f'(x) = 14x
5. f'(x) = 2x