Exercises - Higher Order Derivatives

  1. Find $y''$ in simplest form for each:

    1. $\displaystyle{y = x^{1/3} (x+1)}$

    2. $\displaystyle{y = \frac{x^2 - 1}{(x+4)^2}}$

    3. $\displaystyle{y = \frac{x^2-4}{x^2+1}}$

    4. $\displaystyle{y = \frac{2x^3}{x^3+1}}$

    5. $\displaystyle{y = \sqrt{x^2+9}}$

    6. $\displaystyle{y = \frac{6x}{x^2+1}}$

    7. $\displaystyle{y = \frac{2x^3}{x+1}}$

  2. Find $y'''$ in simplest form for each:

    1. $\displaystyle{y = 4x^3 - 3e^x - \sin x}$

    2. $\displaystyle{y = e^{\ln \cos x} - \ln \left( \frac{x}{e^x} \right)}$