Question

If y=3/x then y'=?

A)-y/x
B)y/x
C)-x/y
D)-3x/y
E)-y/3x

Answer 1

`y=(3)/(x)\\\\\\ y'=\left((3)/(x)\right)'=(3\cdot x^(-1))'=3\cdot(x^(-1))'=3\cdot(-1)\cdot x^(-2)=-3\cdot x^(-2)=\\\\\\=-(3)/(x^2)=-(3)/(x\cdot x)=-(3)/(x)\cdot(1)/(x)=-y\cdot(1)/(x)=-(y)/(x)`

Answer (A)