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Find the derivative of [ax^2+bx+c]/[px^2...

Find the derivative of `[ax^2+bx+c]/[px^2+qx+r]`

Text Solution

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Let `y = (ax^2+bx+c)/(px^2+qx+r)`
`:. dy/dx = ((px^2+qx+r)(2ax+b)-(ax^2+bx+c)(2p+q))/((px^2+qx+r)^2)`
`=(2apx^3+2aqx^2+2arx+bpx^2+bqx+br-2apx^3-2bpx^2-2pcx-aqx^2-bqx-cq)/((px^2+qx+r)^2)`
`:. dy/dx = ((aq-bp)x^2+(2ar+bq-2pc-pq)x+(br-cq))/(px^2+qx+r)^2`
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