Differentiate f(x)=3x2−5xx2−1
By applying Long Division, we have
Thus,
f(x)=3x2−5xx2−1=3+−5x+3x2−1
Then, by taking the derivative using Quotient Rule, we obtain
f′(x)=ddx(3)+ddx[−5x+3x2−1]f′(x)=0+(x2−1)⋅ddx(−5x+3)−(−5x+3)⋅ddx(x2−1)(x2−1)2f′(x)=(x2−1)(−5)−(−5x+3)(2x)(x2−1)2f′(x)=−5x2+5+10x2−6x(x2−1)2=5x2−6x+5(x2−1)2
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