Answer to Question #214028 in Calculus for sbuda

Question

Differentiate the following with regard to x

y=2x-8/5-3x^2

Answer 1

$y={2x-8\over 5-3x^2}$

let $u=2x-8\implies {du\over dx}=2$

let $v=5-3x^2 \implies {dv\over dx}=-6x$

In this case, we use the quotient rule of differentiation as follows

${dy\over dx}={({du\over dx}\times v)-(u\times{dv\over dx})\over v^2}$

$={2(5-3x^2 )-(2x-8)\times(-6x)\over (5-3x^2)^2}$

$={2(5-3x^2 )+6x(2x-8)\over (5-3x^2)^2}$

$={10-6x^2 +12x^2-48x\over (5-3x^2)^2}$

$={10+6x^2 -48x\over (5-3x^2)^2}$