What is the derivative of #y=(x^5)/(1-x^6)#?

1 Answer
Jim G.
Jul 9, 2017

#dy/dx=(x^(10)+5x^4)/(1-x^6)^2#

Explanation:

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

#"given " y=(g(x))/(h(x))" then"#

#dy/dx=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"#

#g(x)=x^5rArrg'(x)=5x^4#

#h(x)=1-x^6rArrh'(x)=-6x^5#

#rArrdy/dx=((1-x^6)(5x^4)-x^5(-6x^5))/(1-x^6)^2#

#color(white)(rArrdy/dx)=(5x^4-5x^(10)+6x^(10))/((1-x^6)^2#

#color(white)(rArrdy/dx)=(x^(10)+5x^4)/(1-x^6)^2#

Related questions
Impact of this question
678 views around the world
You can reuse this answer
Creative Commons License