Recall the derivative of $f(x)$ is written many different ways. For example $f'(x)$, $dy/dx$ or

$$\frac{d}{dx}[f(x)].$$

No matter how you slice it though, it is the function which gives the slope of the tangent line to $f(x)$ at the point on the graph $(x,f(x))$. Practice finding derivatives on the functions below. For each problem, you should identify the rule or rules you used. If you doubt your answer, try graphing the function to see if the derivative function you found could possibly be the real derivative.

1. $f(x) = \pi$. Find $f'(2\pi)$

2. $f(x) = 16x$. Find $f'(x)$.

3. $f(x) = 16 x^2 - 32 x + 1/x$. Find $f'(x)$.

4. $f(x) = - 16x^2 + 100 x - 250$. Find $f'(x)$, $f''(x)$ (The derivative of $f'(x)$.)

5. $f(x) = \sqrt{x}$ Find $f'(x)$.

6. $f(x) = x (x+5)$. Find $f'(x)$.

7. $f(x) = x^{10} \sin(x)$. Find $f'(x)$.

8. $f(x) = x \sin(x) \sqrt{x}$. Find $f'(x)$.

9. Find $f'(x)$ where

   $$f(x) = \frac{x^2 - 2}{x^2 + 2}.$$

10. Find $f'(x)$ where

    $$f(x) = \frac{\sqrt{x} + \sin(x)}{\cos(x)}$$

11. $f(x) = \sqrt{x^2 + 2}$. Find $f'(x)$.

12. $f(x) = \sin(x^2)$. Find $f'(x)$.

13. $f(x) = \sin^2(x)$. Find $f'(x)$.

14. $f(x) = \sin(\cos(\sin(x)))$. Find $f'(x)$.

15. Find $f'(x)$ where

    $$f(x) = \frac{\sqrt{x^2 + 2}}{x^2 + \sqrt{\sin(x)}}$$