Is there a quick way to simplify this?
f"(x)=((x²+3)²(-36)-(-36x)(2)(x²+3)(2x))/(x²+3)⁴

Question

Is there a quick way to simplify this?
f"(x)=((x²+3)²(-36)-(-36x)(2)(x²+3)(2x))/(x²+3)⁴

kainui · Answer

Get good at algebra or use the product rule instead of the quotient rule always.

zehanz · Answer

Written as a proper formula:$$f"(x)=\frac{ (x^2+3)^2 \cdot -36--36x \cdot 2(x^2+3) \cdot 2x }{ (x^2+3)^4 }$$You see that x^2+3 is a factor of the numerator and the denominator, so it cancels:$$f"(x)=\frac{ (x^2+3) \cdot -36+36x \cdot 2 \cdot 2x }{ (x^2+3)^3 }$$Also, 36 can be factored out in the numerator :$$f"(x)=\frac{ 36(4x^2-(x^2+3))}{ (x^2+3)^3 }$$Now just simplify the numerator a little more:$$f"(x)=\frac{ 36(3x^2-3)}{ (x^2+3)^3 }=\frac{ 108(x^2-1)}{ (x^2+3)^3 }=\frac{ 108(x+1)(x-1)}{ (x^2+3)^3 }$$That's about the quickest, I'd say...

anonymous · Answer

Awesome, thats exactly what I was looking for I appreciate the help.

zehanz · Answer

YW!