Question

The following function. g(x)=2x^(2)+(4,000)/(x)+6.Find the dferivative of the function.

Answer 1

The derivative of the function g(x) = 2x^2 + (4,000)/x + 6 is g'(x) = 4x - 4,000/x^2.

Step-by-step explanation:

You're tasked with finding the derivative of the function g(x) = 2x2 + (4,000)/x + 6. This is a calculus problem where we use the rules for differentiation.

Let's find the derivative step by step:

1. Differentiate 2x2, which is a power function. Using the power rule, which is d/dx(xn) = nxn-1, we get the derivative 4x.
2. Now differentiate (4,000)/x. This is a quotient so you can use the derivative of x-1 which is -x-2. Therefore, its derivative is -4,000x-2 or -4,000/x2.
3. The derivative of the constant 6 is 0, because the derivative of any constant is 0.

Putting it all together, the derivative of g(x) is g'(x) = 4x - 4,000/x2.