(1)/((x^(2)+3)^(2))...

`(1)/((x^(2)+3)^(2))`

Text Solution

Verified by Experts

Let `y = (1)/((x^(2)+3)^(2))`
`therefore (dy)/(dx)=(d)/(dx)(x^(2)+3)^(-2)`
`=-2(x^(2)+3)^(-3).(d)/(dx)(x^(2)+3)`
`=(-2)/((x^(2)+3)^(3)).(2x+0)=(-4x)/((x^(2)+3)^(3))`

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If x^(2) + 1 = 2 x then the value of (x^(4) +(1)/( x^(2)))/(x^(2) - 3 x + 1) is

`-2`

If x-(1)/(x)=1 , then the value of (x^(4)-(1)/(x^(2)))/(3x^(2)+5x-3) is

`(1)/(4)`

`(1)/(2)`

`(3)/(4)`

Find the product of ((1)/(2)x^(2)-(1)/(3)y^(2))and((1)/(2)x^(2)+(1)/(3)y^(2))

`(1)/(9)y^(4)-(1)/(4)x^(4)`

`(1)/(4)x^(4)-(1)/(9)y^(4)`

`4x^(2)-9y^(4)`

`(1)/(y)x^(4)-(1)/(9)y^(9)`