Question

Differentiate y=2x+200/x with respect to x

Answer 1

`(dy)/(dx ) = 2 - \frac{200}{ {x}^(2) }`

Explanation:

`the \: equation \: can \: be \: rewriten \: as \\ y = 2x + 200 {x}^( - 1) \\ \\ now \: differentiate \: the \: equation\ \\ (dy)/(dx) = 2 - 200 {x}^( - 2) \\ (dy)/(dx) = 2 - \frac{200}{ {x}^(2) }`

Answer 2

Hello,

`\boxed{y'=2-(200)/(x^2) }\\`

Explanation:

`(f(x)+g(x))'=f'(x)+g'(x)\\\\(2x)'=2*(x)'=2*1=2\\\\((200)/(x) )'=200*(x^(-1))'=200*(-1)*x^(-1-1))=-(200)/(x^2) \\\\\\\boxed{y'=2-(200)/(x^2) }\\`