These problems problems are to get you to look back at your calculus $1$ notes and see if you can remember how to do them. You could also get a calculus $1$ textbook for help.

Let

$f(x)=\frac{5x^3+3\sqrt[\phantom{2}]{x}}{x}$

find $f^{\text{'}}(x).$

$2.$ Find

$\frac{d}{dx}\sqrt[\phantom{2}]{5x^2+\sqrt[\phantom{2}]{x}}$

Find the equation of the tangent line of:

$y=cos(x)+sin(x)$

at $(\frac{}{4},\sqrt[\phantom{2}]{2})$ and $(\frac{}{3},\frac{\sqrt[\phantom{2}]{3}+1}{2})$

$4.$ If the position of a particle at time $t$ is given by:

$s(t)=\sqrt[\phantom{2}]{t}{e}^t$

find the acceleration of the particle at time $t=4.$

$5.D_x(2^{x^2+1})$

$6.D_x(ln(sin(tan(x))))$

Note $D(tan(x))=se{c}^2(x)=1+ta{n}^2(x).$

$7.$ Sketch a graph of a function that satisfies the following table. Note one of the $f^{\text{'}\text{'}}$ is impossible, figure out which one is impossible and eliminate it$.$

$\backslash$table