Lab $3$ problem

Q$1$: Use the code snippets above, plot the function $y(t)=e^{-t}sin(t),$ its derivative $w(t)=y^{\text{'}}=-e^{-t}sin(t)+e^{-t}cos(t)$ on the same plot from $1t10.$ Try with both a step of $h=1$ and $h=0\mathrm{.}1$ to notice the difference, although the example graph below is just the $h=0\mathrm{.}1$ case.

Q$2.$ Then, use finite difference to approximate $y^{\text{'}},$ you can use the code snippet above using a for loop or vectorization. Plot with the step size $h$ to be $1$ and $0\mathrm{.}1$ in two plots.

Please answer with codes