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