Question

(2x^3-4)';8x^4+1/x^5.

Answer 1

Объяснение:

2x^3-4

2х^-1

2×1/х

2/х

8х^4+1/х^5

8х^5/х^5

8

Answer 2

To find the derivative of the function (2x^3 - 4)', we can apply the power rule of differentiation. The power rule states that for any function of the form f(x) = ax^n, the derivative is given by f'(x) = nax^(n-1).

Let's differentiate each term separately:

For the term 2x^3, we have a = 2 and n = 3. Applying the power rule, the derivative of 2x^3 is:

(2x^3)' = 3(2)x^(3-1) = 6x^2

For the term -4, since it is a constant, its derivative is zero.

Therefore, the derivative of the function (2x^3 - 4) is:

(2x^3 - 4)' = 6x^2 + 0 = 6x^2

Now, let's find the derivative of the function 8x^4 + 1/x^5. We can differentiate each term separately using the power rule and the quotient rule.

For the term 8x^4, we have a = 8 and n = 4. Applying the power rule, the derivative of 8x^4 is:

(8x^4)' = 4(8)x^(4-1) = 32x^3

For the term 1/x^5, we can rewrite it as x^(-5). Applying the power rule, the derivative of x^(-5) is:

(x^(-5))' = -5x^(-5-1) = -5x^(-6) = -5/x^6

Therefore, the derivative of the function 8x^4 + 1/x^5 is:

(8x^4 + 1/x^5)' = 32x^3 - 5/x^6