Question #0d05a

1 Answer
Jim G.
Sep 2, 2017

#h''(x)=60/(x+5)^3#

Explanation:

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

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

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

#f(x)=x^2-xrArrf'(x)=2x-1#

#g(x)=x+5rArrg'(x)=1#

#rArrh'(x)=((x+5)(2x-1)-(x^2-x))/(x+5)^2#

#color(white)(rArrh'(x))=(x^2+10x-5)/(x+5)^2#

#"to obtain "h''(x)" differentiate "h'(x)#
#"using the "color(blue)"quotient rule"#

#f(x)=x^2+10x-5rArrf'(x)=2x+10=2(x+5)#

#g(x)=(x+5)^2rArrg'(x)=2(x+5)#

#rArrh''(x)=(2(x+5)^3-2(x+5)(x^2+10x-5))/(x+5)^4#

#color(white)(rArrh''(x))=((x+5)[2(x+5)^2-2(x^2+10x-5)))/(x+5)^4#

#color(white)(rArrh''(x))=60/(x+5)^3to(A)#

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