What is the second derivative of #f(x)=x^2/(x+3) #?

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Answer 1 · 2016-11-19T15:36:55

Differentiate once, and then differentiate again.

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

#f'(x) = (2x^2 + 6x - x^2)//(x + 3)^2#

#f'(x) = (x^2 + 6x)/(x^2 + 6x + 9)#

Differentiate once more.

#f''(x) = ((2x + 6)(x^2+ 6x + 9) - ((2x + 6)(x^2 + 6x)))/(x^2 + 6x + 9)^2#

You can simplify this further, but I'll leave the algebra up to you.

Hopefully this helps!