derivation of x2/x3+1
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Hope this helps.See the attached file above.
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Let f(x)=x+12−3x−1x2
f′(x)=dxd(x+12)−dxd(3x−1x2)
By quotient rule
f′(x)=[(x+1)2(x+1)dxd(2)−2dxd(x+1)]−[(3x−1)2(3x−1)dxd(x2)dxd(3x−1)
(x+1)(0)−2(1)]−[(3x−1)2(3x−1)(2x)−(x2)(3)]
=(x+1)2−2−[(3x−1)26x2−2x−3x2]
=(x+1)2−2−[(3x−1)23x2−2x]
=(x+1)2−2−(3x−1)2x(3x−2)
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