Friday, June 13, 2014

Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 46

Differentiate f(x)=3x25xx21
By applying Long Division, we have



Thus,
f(x)=3x25xx21=3+5x+3x21

Then, by taking the derivative using Quotient Rule, we obtain

f(x)=ddx(3)+ddx[5x+3x21]f(x)=0+(x21)ddx(5x+3)(5x+3)ddx(x21)(x21)2f(x)=(x21)(5)(5x+3)(2x)(x21)2f(x)=5x2+5+10x26x(x21)2=5x26x+5(x21)2

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