Simplification question?

I’m having problems simplifying  f’’(x). f’(x) = 18x/(x^2+3)^2. Could someone show me the way?

3 Answers

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  • MyRank
    Lv 6
    4 weeks ago

    f’(x) = 18x / (x²+3)²

    f”(x) = d/dx (18x)(x²+3)² - (18x)d/dx(x²+3)² / ((x²+3)²)²= 18(x²+3)² - 18x x 2(x²+3)(2x) / ((x² + 3)²)²= 18(x²+3)² - 72x²(x²+3) / ((x²+3)²)²18(x²+3)[x²+3-4x²] / ((x²+3)²)²= 18(x²+3)[3(1-x²)] / (x²+3)⁴= 18[3(1-x²)] / (x²+3)³.

  • Ash
    Lv 7
    4 weeks ago

    f'(x) = 18x/(x²+3)²

    f"(x) = derivative of f'(x)

    Use quotient rule  d(f(x)/g(x)) = [g(x) df(x) - f(x) dg(x)]/ (g(x))²

    f"(x) = [(x²+3)² d(18x) - 18x d(x²+3)²] / ((x²+3)²)²

    f"(x) = [(x²+3)² * 18  -  18x*2(x²+3) d(x²+3) ] / (x²+3)⁴

    f"(x) = [18(x²+3)² - 36x (x²+3) * 2x ] / (x²+3)⁴

    f"(x) = [18(x²+3)² - 72x² (x²+3) ] / (x²+3)⁴

    f"(x) = (x²+3)[18(x²+3) - 72x² ] / (x²+3)⁴

    f"(x) = (18x²+54 - 72x² ) / (x²+3)³

    f"(x) = (54 - 54x²) / (x²+3)³

    f"(x) = 54(1 - x²) / (x²+3)³

      

  • rotchm
    Lv 7
    4 weeks ago

    First, evaluate the derivative of 18x/(x^2+3)^2. What procedure you are using? Whats the result?

    • Lv 4
      4 weeks agoReport

      good points; also, maybe note that f'(x) = 18x(x^2+3)^(-2) which might lend to derivation by Chain Rule method, though maybe watch out for possible points re x= +/- 3^(1/2), since +/- [3^(1/2)]^2 => +/-(3, => etc...

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