Question

Hey I’m confused by this question can anyone help

Answer 1

Explanation:

difference quotient

`(dy)/(dx) = \lim_(h\to 0) (f(x+h)-f(x))/((x+h)-x) = \lim_(h \to ) (f(x+h)-f(x))/(h)`

`(dh)/(dx) = \lim_(h \to 0) ((1)/(2(x+h)) -(1)/(2x) )/(h) \\(dh)/(dx) = \lim_(h \to 0)((2x-2x-2h)/(2x(2(x+h))) )/(h) \\(dh)/(dx) = \lim_(h\to 0)(-2h)/(4hx(x+h)) \\(dh)/(dx) = \lim_{h \to 0(-1)/(2x(x+h)) \\`

`(dh)/(dx) =-(1)/(2x(x+0)) \\(dh)/(dx) =-(1)/(2x^2)`