What is the derivative of dS=x^2+ 5488/x?...

To find the derivative of the function dS = x^2 + 5488/x, we can follow the general rules of differentiation.

Step 1: Identify the terms in the function. In this case, we have two terms: x^2 and 5488/x.

Step 2: Apply the power rule for differentiation to the term x^2. For any term of the form x^n, the derivative is obtained by multiplying the coefficient (n) by the term itself and then decreasing the power of x by 1. In this case, the derivative of x^2 is 2x.

Step 3: Apply the quotient rule for differentiation to the term 5488/x. For any term of the form a/x, the derivative is obtained by subtracting the product of the derivative of x (which is 1) and the term itself from the product of the constant (a) and the derivative of 1/x (which is -1/x^2). In this case, the derivative of 5488/x is (-5488/x^2).

Step 4: Sum up the derivatives of both terms to find the overall derivative of the function. In this case, adding the derivatives of 2x and (-5488/x^2) gives us the final derivative of dS.

Therefore, the derivative of dS = x^2 + 5488/x is dS' = 2x - 5488/x^2.