Question

What is the derivative of `y=x/(5-3x)`?

Answer 1

`5/(5-3x)^2`

Explanation:

For this we have to use the quotient rule which is,
`(f/g)prime=(fprime*g-f*gprime)/g^2`

Where
`f=x`
`fprime=1`
`g=(5-3x)`
`gprime=-3`

So now we plug it into the formula
`((1)*(5-3x)-[x(-3)])/(5-3x)^2`

Which simplifies to
`((5-3x)-(-3x))/(5-3x)^2`

`(5-3x+3x)/(5-3x)^2`

`5/(5-3x)^2` which is the answer.