Simple derivative

[AGlas9837]

I'm given S=2x+288/x and told the derivative is dS/dx = 2-288/x^2. I'm not following how you get this derivative here. (This has to do with an optimization problem where you are looking for a minimum sum.)

 

[royhaas]

Use the power rule.

 

[soroban]

Hello, AGlas9837!

You've new at differentiation?

$\displaystyle \text{I'm given }S\:=\:2x+\frac{288}{x}\text{ and told the derivative is: }\frac{dS}{dx} \:=\: 2-\frac{288}{x^2}$

Exactly where is your difficulty?


$\displaystyle \text{The derivative of }2x\text{ is }2.$


$\displaystyle \text{For the derivative of -}\frac{288}{x}$

. . $\displaystyle \text{(1) use the Quotient Rule, or}$

. . $\displaystyle \text{(2) use the Power Rule on -}288x^{-1}$

 

[AGlas9837]

I see now...using the quotient rule it makes sense. Thank you! (First semester of calculus....all of my algebra was taken a long time ago)