A condensed reference card covering every key derivative formula, the most common exam question types, quick solution methods, and the 5 things you must remember before you sit down to write. Print it, study it tonight, ace it tomorrow.
This cram sheet is designed to print cleanly on a single page — formulas, strategies, and tips all at once.
| Rule | Formula |
|---|---|
| Constant | \(\tfrac{d}{dx}[c]=0\) |
| Power | \(\tfrac{d}{dx}[x^n]=nx^{n-1}\) |
| Constant Multiple | \(\tfrac{d}{dx}[cf]=cf'\) |
| Sum / Difference | \((f\pm g)'=f'\pm g'\) |
| Product | \((fg)'=f'g+fg'\) |
| Quotient | \(\!\left(\tfrac{f}{g}\right)'\!=\tfrac{f'g-fg'}{g^2}\) |
| Chain | \(\tfrac{d}{dx}[f(g)]=f'(g)\cdot g'\) |
| \(f(x)\) | \(f'(x)\) |
|---|---|
| \(\sin x\) | \(\cos x\) |
| \(\cos x\) | \(-\sin x\) |
| \(\tan x\) | \(\sec^2 x\) |
| \(\sec x\) | \(\sec x\tan x\) |
| \(\csc x\) | \(-\csc x\cot x\) |
| \(\cot x\) | \(-\csc^2 x\) |
| \(f(x)\) | \(f'(x)\) |
|---|---|
| \(\arcsin x\) | \(\tfrac{1}{\sqrt{1-x^2}}\) |
| \(\arccos x\) | \(\tfrac{-1}{\sqrt{1-x^2}}\) |
| \(\arctan x\) | \(\tfrac{1}{1+x^2}\) |
| \(e^x\) | \(e^x\) |
| \(a^x\) | \(a^x\ln a\) |
| \(\ln x\) | \(\tfrac{1}{x}\) |
| \(\sin^2x+\cos^2x=1\) |
| \(1+\tan^2x=\sec^2x\) |
| \(\sin 2x=2\sin x\cos x\) |
| \(\cos 2x=\cos^2x-\sin^2x\) |
| \(\tfrac{d}{dx}[x^n e^x]=x^{n-1}e^x(n+x)\) |
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The cram sheet is organized into four zones: