1.

Find the derivative of the following functions (it is to be understand that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): `(ax+b)/(px^(2)+qx+r)`

Answer» Let `y=(ax+b)/(px^(2)+qx+r)`
`rArr(dy)/(dx)=(d)/(dx)((ax+b)/(px^(2)+qx+r))` ltbr. `(px^(2)+qx+r)(d)/(dx)(ax+b)`
`-(ax+b)(d)/(dx)(px^(2)+qx+r)`
`(px^(2)+qx+r)^(2)`
`=(px^(2)+qx+r)^(2)`
`(apx^(2)+aqx+ar)`
`=-(2apx^(2)+aqx+2bpx+bq)`
`(px^(2)+qx+r^(2))^(2)`


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