# Existing functions to use

import numpy as $np$

$a=-3$

$b=3$

$y=$ lambda $x$:$np*cos(x)+np*cos(5^{**}x)-np*sin(3^{**}x)$

$yp=x$:$-np*sin(x)-5^{**}np*sin(5^{**}x)-3^{**}np*cos(3^{**}x)$

$yi=$ lambda $x$:$np*sin(x)+np*sin\frac{5^{**}x}{5}+np*cos\frac{3^{**}x}{3}$

$h1=\frac{1}{3}$

$x1=np.$linspace $(a,b,19)$

$h2=\frac{1}{100}$

$x2=np*linspace(a,b,601)$

$c=yi(a)$

Question: Calculate the derivative and integral for y$1$ and y$2.$ Plot them compared to known actual answers. Check R$^2$ fit too. need code in python. that easy for a begineer to understand