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Review of Differentiation, Math 223

Find the first derivatives of the following functions. Use proper notation.

1. $f(x)=\frac{x^2+bx+c}{a}$ 2. $y(t)=\frac{3}{\sqrt{t}+2}$ 3. $z = \frac{\sec(w)}{1 + \tan(w)}$

4. $f(x)=x^2\cos(x)+3\sin(4)$ 5. $v=\sqrt[3]{\tan(5t)}$ 6. $t(y)=\left(\frac{y-5}{2y+1}\right)^3$

7. $y(\theta)=\ln (\sin(\pi \theta))$ 8. $f(t)=\exp(1/t)$ 9. $f(\theta)=e^{-\theta}\cos(b\theta)$

10. $z=5^{\sin(x)}$ 11. $y = \frac{1}{\arctan(x)}$ 12. $f(t)=\arcsin(t^2)$

13. $v(r)=\pi^r \cdot r^\pi$ 14. $y = e^{\sqrt{x}}(x^2+1)$ 15. $z=\log(10^{2x})$

16. $f(m)=\frac{1}{\sec(2m)}$ 17. $f(\Gamma)=\frac{\beta \Gamma + \Gamma^6}{1 - \beta}$ 18. $s = \frac{\ln (t)}{1 + \ln(t)}$

19. $y = \frac{x^3}{(1-x)^2}$ 20. $f(t) = \frac{\sqrt{t}+4}{t}$ 21. $y=e^{\ln(x+1)}$

Vector Calculus
1999-01-29

1.	$f(x)=\frac{x^2+bx+c}{a}$	2.	$y(t)=\frac{3}{\sqrt{t}+2}$	3.	$z = \frac{\sec(w)}{1 + \tan(w)}$
4.	$f(x)=x^2\cos(x)+3\sin(4)$	5.	$v=\sqrt[3]{\tan(5t)}$	6.	$t(y)=\left(\frac{y-5}{2y+1}\right)^3$
7.	$y(\theta)=\ln (\sin(\pi \theta))$	8.	$f(t)=\exp(1/t)$	9.	$f(\theta)=e^{-\theta}\cos(b\theta)$
10.	$z=5^{\sin(x)}$	11.	$y = \frac{1}{\arctan(x)}$	12.	$f(t)=\arcsin(t^2)$
13.	$v(r)=\pi^r \cdot r^\pi$	14.	$y = e^{\sqrt{x}}(x^2+1)$	15.	$z=\log(10^{2x})$
16.	$f(m)=\frac{1}{\sec(2m)}$	17.	$f(\Gamma)=\frac{\beta \Gamma + \Gamma^6}{1 - \beta}$	18.	$s = \frac{\ln (t)}{1 + \ln(t)}$
19.	$y = \frac{x^3}{(1-x)^2}$	20.	$f(t) = \frac{\sqrt{t}+4}{t}$	21.	$y=e^{\ln(x+1)}$