Question

F(x)=4x+1/x+3 производные

Answer 1

Если числитель 4x+1, а знаменатель x+3, то:

f'(x)= ((4x+1)'(x+3)-(4x+1)(x+3)')/(x+3)²= (4(x+3)-(4x+1))/(x+3)²= (4x+12-4x-1)/(x+3)²= 11/(x+3)²

если 4x+(1/x) +3, то:
f'(x)= 4- (1/x²)

Answer 2

1) f(x)= 4x+1/x+3

f '(x)= 4+(-1/x^2) +0 = 4-1/x^2

2)f(x)= (4x+1)/(x+3)

f '(x)= [ 4*(x+3)-(4x+1)*1 ] / (x+3)^2 = [4x+12-4x-1]/(x+3)^2 = 11/(x+3)^2

Answer 3

To find the derivatives of the function F(x) = 4x + 1/x + 3, we'll need to apply differentiation rules step by step. Since this function is a combination of two terms, one being a polynomial (4x) and the other involving a rational expression (1/x), we'll use the sum/difference rule and the power rule for differentiation.

The sum/difference rule states that the derivative of a sum (or difference) of functions is the sum (or difference) of their derivatives.

The power rule states that the derivative of x^n with respect to x is n*x^(n-1).

Let's calculate the derivatives step by step:

1. Derivative of the first term (4x): The derivative of 4x with respect to x is simply 4 since the power of x is 1.

d/dx (4x) = 4

2. Derivative of the second term (1/x): The derivative of 1/x with respect to x is -1/x^2.

d/dx (1/x) = -1/x^2

Now, we can rewrite the original function with the derivatives we've calculated:

F(x) = 4x + 1/x + 3

d/dx (F(x)) = d/dx (4x) + d/dx (1/x) + d/dx (3)

d/dx (F(x)) = 4 - 1/x^2 + 0

Finally, the derivative of the function F(x) is:

d/dx (F(x)) = 4 - 1/x^2