Question

(2x-3)’=2 т к (2x)’=c (Sin x)’= cosx (-3)’=0

Answer 1

Відповідь:Используя степенное правило дифференцирования, имеем:

(2x-3)’ = 2

потому что производная 2x равна 2, а производная -3 (константа) равна 0.

Что касается второй части вопроса, то имеем:

(Sin x)’ = cos x

потому что производная от sin x равна cos x согласно формуле производной для тригонометрических функций.

Наконец, мы имеем:

(-3)’ = 0

потому что производная константы всегда равна 0.

Покрокове пояснення:

Answer 2

Let's differentiate each expression step by step:

1. (2x - 3)'

To differentiate this expression, we can use the power rule, which states that the derivative of x^n with respect to x is equal to n*x^(n-1). Applying this rule, we differentiate each term separately:

d(2x)/dx = 2 d(-3)/dx = 0

Therefore, (2x - 3)' = 2.

2. (2x)'

Since (2x) is a term with a constant coefficient, the derivative of (2x) with respect to x is simply the coefficient, which is 2. Therefore, (2x)' = 2.

3. (sin x)'

To differentiate the sine function, we use the chain rule. The derivative of sin(x) with respect to x is equal to cos(x). Therefore, (sin x)' = cos x.

4. (-3)'

Since -3 is a constant term, its derivative with respect to x is 0. Therefore, (-3)' = 0.

To summarize:

• (2x - 3)' = 2
• (2x)' = 2
• (sin x)' = cos x
• (-3)' = 0