How do you differentiate f(x)=x^6/(x-6)f(x)=x6x−6 using the quotient rule?

1 Answer
Jim G.
Aug 12, 2018

f'(x)=(5x^6-36x^5)/(x-6)^2

Explanation:

"given "f(x)=(g(x))/(h(x))" then"

f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larrcolor(blue)"quotient rule"

g(x)=x^6rArrg'(x)=6x^5

h(x)=x-6rArrh'(x)=1

f'(x)=(6x^5(x-6)-x^6)/(x-6)^2

color(white)(f'(x))=(5x^6-36x^5)/(x-6)^2

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