Exercise $1$: Stencil operations & slicing f$($x$)=(($x$^(2)+4$x$+5)/($x$+2$e$^($x$)))^(2$x$)$ Hint: Remember the use of the lambda function. # YOUR CODE HERE raise NotImplementedError$()$ b$)$ Calculate the derivative of f$($x$)$ with the central difference formula $($below$),$ save result in the variable fprime $.$ f$^(\text{'})($x$\_($i$))$~~$($f$($x$\_($i$+1))-$f$($x$\_($i$-1)))/(2\backslash$Delta x$)$ # YOUR CODE HERE raise NotImplementedError$()$ We add to y a scaled noise as follows # RUN THIS CELL. DO NOT MODIFY. numpy. random. seed $(42)$ numpy. random. rand $($y$*$size$)**2-1$ fprime$\_$noise $=$ numpy.gradient $($yn$,0\mathrm{.}001)$ c$)$ Next step is to compute smoothed values of the noisy data $($yn$)$ by using the average of a point with its two nearby neighbors. Use slicing to compute the following, save your result in a variable called y$\_$smooth $.$ y$\_($smooth $)=($y$\_($i$-1)+$y$\_($i$)+$y$\_($i$+1))/(3)$ # YOUR CODE HERE raise NotImplementedError$()$ d$)$ Using an average of $5$ points as follows: y$\_($smooth $\_(()5))=($y$\_($i$-2)+$y$\_($i$-1)+$y$\_($i$)+$y$\_($i$+1)+$y$\_($i$+2))/(5)$ Save your result in a variable called y$\_$smooth$\_5.$ # YOUR CODE HERE raise NotImplementedError$()$