y=x/(2x-3) then find (d^2y)/(dx^2)?

2 Answers
May 3, 2018

(d^2y)/(dx^2)=12/(2x-3)^3

Explanation:

.

y=x/(2x-3)

dy/dx=((2x-3)(1)-x(2))/(2x-3)^2=(2x-3-2x)/(2x-3)^2=(-3)/(2x-3)^2

(d^2y)/(dx^2)=((2x-3)^2(0)-(-3)(2)(2x-3)(2))/(2x-3)^4=(12(2x-3))/(2x-3)^4=12/(2x-3)^3

May 3, 2018

:.(d^2y)/(dx^2)=(12)/((2x-3)^3)

Explanation:

Here,

y=x/(2x-3)

"Using "color(blue) "Quotient Rule:" ( Diff.w.r.t. x.)

=>(dy)/(dx)=((2x-3)d/(dx)(x)-xd/(dx)(2x-3))/((2x-3)^2)

=>(dy)/(dx)=((2x-3)(1)-(x)(2))/((2x-3)^2)

=>(dy)/(dx)=(2x-3-2x)/((2x-3)^2)
=>(dy)/(dx)=(-3)/((2x-3)^2)

Again "Using "color(blue) "Quotient Rule:" ( Diff.w.r.t. x.)

(d^2y)/(dx^2)=((2x-3)^2(0)-(-3)(2(2x-3)2))/((2x- 3)^4)

=>(d^2y)/(dx^2)=(3xx2xx2(2x-3))/((2x-3)^4)

=>(d^2y)/(dx^2)=12/((2x-3)^3)