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If y=x-x^2, then the derivative of y^2 w...

If `y=x-x^2`, then the derivative of `y^2` w.r.t `x^2` is

A

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

B

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

C

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

D

`2x^(2)-3x-1`

Text Solution

Verified by Experts

The correct Answer is:
B
`:'y=x-x^(2)`
`:.(dy)/(dx)=1-2x`
Now `(d(y^(2)))/(d(x^(2)))=((d(y^(2)))/(dx))/(d((x^(2)))/(dx))`
`=(2y(dy)/(dx))/(2x)=y/x(1-2x)`
`=(1-x)(1-2x)`
`=1-3x+2x^(2)`
`=2x^(2)-3x+1`
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