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

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Answer 1 · 2018-03-15T17:04:23

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

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.

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