I got this answer from someone else so I’m not sure this is correct but I really hope it helps...
Step-by-step explanation:
Look for patterns in the derivatives.
y=cos2x
y'=-2sin2x
y''=-4cos2x
y'''=8sin2x
y''''=16cos2x
Notice that sin and cos alternate every derivative. Also, they alternate positive and negative every 2 derivatives.
The constant is just 2^(derivative#).
Every odd derivative has sin and every even derivative has cos, so you know that the 30th derivative will be cos.
If you follow the pattern of negatives and positives, you find that the 30th derivative will be negative.
y^(30)= -2^30cos2x
y^(30)= -1073741824cos2x
10^4+6x=8 that’s one equation I made up :)
In order to make a table, we sample some x values (whichever we want), and we compute the expression for those value. Each x value will yield a unique y value.
If you need this table to graph the function, you'll only need two points, since this is a line, and having two points you just need to connect them.
Here are some samples, feel free to make more if you need to:
So, we have the following table
