[Verse 1]
Power rule starts simple, take the x to n
Drop the power down, subtract one from the end
n times x to the n-minus-one, that's the way
Gravity of calculus, works every day
[Chorus]
e to the x stays e to the x, magic in the math
Natural log gives one over x, follow the path
Sine becomes cosine, cosine flips to negative sine
Tangent turns to secant squared, derivatives align
[Verse 2]
The exponential function has a secret to tell
Its rate of change is itself, under its own spell
When populations multiply or money compounds fast
e to the x derivative makes the pattern last
[Chorus]
e to the x stays e to the x, magic in the math
Natural log gives one over x, follow the path
Sine becomes cosine, cosine flips to negative sine
Tangent turns to secant squared, derivatives align
[Verse 3]
Trig functions spinning like a wheel around
Arcsine gives one over root one minus x squared
Arctangent's derivative is one plus x squared beneath
These inverse functions have their own relief
[Bridge]
When the base is a not e, multiply by natural log of a
a to the x times ln a, that's the formula
Every function has its fingerprint when differentiation calls
Master these atomic pieces, you can handle them all
[Chorus]
e to the x stays e to the x, magic in the math
Natural log gives one over x, follow the path
Sine becomes cosine, cosine flips to negative sine
Tangent turns to secant squared, derivatives align
[Outro]
From power rule to exponentials, trig functions too
These are your building blocks, derivatives coming through