Calculus Rap

cruisin’ down the highway in your Bentley
going in a straight line, feelin’ like a G
checkin’ out your speed, set at 63
can also use a graph to calculate velocity
say x-axis is time and y is position
velocity easy to get, don’t you listen
just find change of  y over change of x
slope is rise over run or m…that’s a bet
don’t know what I mean, review on my mic
a linear function is like that cruise down the pike
start at b, where time is zero money
y=mx+b, don’t laugh, this ain’t funny
Chorus:
we ain’t drivin’ in a straight line on our next trip
slowin down speeding up as you zip
velocity is changing, with acceleration bro
need to use calculus to find out all the info
non-linear functions are mad confusing
this ain’t no simple graph like y=mx+b
in a linear function, or a straight line
slope is constant each and every time
but we aint drivin’ in a straight line on our next trip
slowin’ down speeding up as you zip
velocity is changing with acceleration bro
need to use calculus to find out all the info
crazy lookin graph with all them curves
slope is always changing, that’s my word
gotta calculate the derivative
at any point on the line, need to find what it is
Chorus
y always relates to x as a function
also called f(x) at this juncture
pick any point on the curve at x
y coordinate will be f(x)
pick another point along the way,  yessur
tiny distance h from where you were
that x coordinate’s gonna be x+h
y will be f(x+h)
slope is change in y over change in x
m=f(x+h)-f(x)
over (x+h)-x
almost done now and you’ll be set
Chorus
that’s numerator over h bro
but now we gotta make that tiny h zero
can’t have a zero in denom so here’s what we do
find limit as h approaches zero dude
it ain’t really hard, think more, don’t complain
calc is the study of instantaneous rate of change
accurate measurements are infinitesimally small
listen to my rhyme, ya ‘bout to know it all
for finding slope now need a derivative
can find it at any point with the function they give
f(x) = x2, piece of cake
to find derivative just plug in for pete’s sake
derivative is dy/dx or f’(x)
same thing, none is better than the rest
that’s (x+h)2 – x2 over h
equals x2 + 2xh
+ h2 – x2 over h
equals 2x+h ya see
but h is approachin’ zero, whatd’a think G
derivative of x2 is 2x finally
Chorus