How do you differentiate #f(x)= (4 x^2 + 5x -8 )/ (x- 1 )# using the quotient rule?

1 Answer
Jim G.
Jan 13, 2017

#f'(x)=(4x^2-8x+3)/(x-1)^2#

Explanation:

differentiate using the #color(blue)"quotient rule"#

#"Given " f(x)=(g(x))/(h(x))" then"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2)color(white)(2/2)|)))#

#"here " g(x)=4x^2+5x-8rArrg'(x)=8x+5#

#"and " h(x)=x-1rArrh'(x)=1#

#rArrf'(x)=((x-1)(8x+5)-(4x^2+5x-8).1)/(x-1)^2#

#=(8x^2-3x-5-4x^2-5x+8)/(x-1)^2#

#=(4x^2-8x+3)/(x-1)^2#

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