# Calculus homework due 3-13-14

Find the derivative of each of the following functions

1. $f(x)=\frac{\sqrt{x}}{x+1}$

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

3. $f(x)=\frac{x^3+x}{4x+3}$

4. $f(x)=e^x(x^2+6x+1)$

5. $f(x)=\frac{x^3}{3}+\frac{1}{e^x}+\frac{\sqrt{x}}{5x^2-x}$

6. $f(x)=(e^x+a)(x^{\frac{2}{3}}-a)$

7. $f(x)=7x^{\frac{7}{5}}+6x^{\frac{5}{4}}+2\sqrt[4]{x}$

8. $f(x)=\sqrt[3]{x}(3+7x)$

9. $f(x)=\frac{\sqrt[3]{x}}{4x^5+x^4+7x^3+5x^2+6x+4}$

10. $f(x)=ce^xx^r$

11. $f(x)=\frac{e^x}{x^a+a}$

12. $f(x)=(x-\sqrt{x})(4x^{\frac{2}{3}}+e)-(\pi-\frac{4x^3}{3})(x^2+y^2)$