Question

Question #0d05a

Answer 1

`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)`