How could this newton's method code be improved to add more functionality and also have an aesthetic user friendly interface with a dashboard showing giving the user the option to input their values for a$,$ b$,$ c$,$ w$,$ v$?$ The graph plotted also should be extended to include the dots of the solutions. Show the new and improved code in its entirety

import numpy as np

import matplotlib.pyplot as plt

# Define the function based on the equation: f$($x$)=$ ax$^$b $-$ e$^($cx$)*$ sin$($wx $+$ v$)$

def f$($x$,$ a$,$ b$,$ c$,$ w$,$ v$)$:

$$ return a$*($x$**$b$)-($np$.$exp$($c$*$x$))*$np$.$sin$(($w$*$x$)+$v$)$ #f$($x$)$

# Define the derivative of the function with respect to x

def fderx$($x$,$ a$,$ b$,$ c$,$ w$,$ v$)$:

$$ return $($a$*$b$*($x$**($b$-1)))-($np$.$exp$($c$*$x$)*($np$.$sin$(($w$*$x$)+$v$)*$c $+$ np$.$cos$(($w$*$x$)+$v$)*$w$))$ #f$\text{'}($x$)$

def newtons$\_$method$($a$,$b$,$c$,$w$,$v$,$x$0,$tolerance$=1$e$-7)$:

$$ x$=$x$0$

$$ for i in range$(100)$:

$$ fx$=$ f$($x$,$ a$,$ b$,$ c$,$ w$,$ v$)$

$$ fpx$=$fderx$($x$,$ a$,$ b$,$ c$,$ w$,$ v$)$

$$ if fpx$==0$:

$$ print$("$The derivative is equal to zero, no solution found"$)$

$$ return None

$$ x$\_$new $=$ x$-$fx$/$fpx

$$ if abs$($x$\_$new$-$x$)<$ tolerance:

$$ return x$\_$new

$$ x$=$x$\_$new

$$ print$("$Exceeded maximum iterations. No solution found."$)$

$$ return None

def multSolns$($a$,$ b$,$ c$,$ w$,$ v$,$ initial$\_$guesses$)$:

$$ solutions$=[]$

$$ for x$0$ in initial$\_$guesses:

$$ solution$=$newtons$\_$method$($a$,$b$,$c$,$w$,$v$,$x$0)$

$$ if solution is not None:

$$ #if solution not in solutions:

$$ if all$($abs$($solution $-$ s$)>1$e$-5$ for s in solutions$)$:

$$ solutions.append$($solution$)$

$$ return solutions

initial$\_$guesses $=[-10,-5,0,5,10]$

#a$,$ b$,$ c$,$ w$,$ v $=1,2,-0\mathrm{.}5,1\mathrm{.}5,0\mathrm{.}5$

a$=$float$($input$("$Please enter a number for a: $"))$

b$=$float$($input$("$Please enter a number for b: $"))$

c$=$float$($input$("$Please enter a number for c: $"))$

w$=$float$($input$("$Please enter a number for w: $"))$

v$=$float$($input$("$Please enter a number for v: $"))$

solutions $=$ multSolns$($a$,$ b$,$ c$,$ w$,$ v$,$ initial$\_$guesses$)$

print$("$Found solutions:", solutions$)$

t$=$ np$.$arange$(-10,10,\mathrm{.}01)$

plt$.$plot$($t$,$f$($t$,$ a$,$ b$,$ c$,$ w$,$ v$))$

plt$.$grid$($True$)$