| \( y \) | \( \displaystyle \frac{dy}{dx} \) |
|---|---|
| Algebraic, Log & Exponential Core | |
| \( x^n \) | \( n\,x^{\,n-1} \) |
| \( a^x \) | \( a^x\ln a \) |
| \( e^x \) | \( e^x \) |
| \( \sqrt{x} \) | \( \frac{1}{2\sqrt{x}} \) |
| \( \frac{1}{x} \) | \( -\,\frac{1}{x^{2}} \) |
| \( \ln x \) | \( \frac{1}{x} \) |
| Trigonometric Trig | |
| \( \sin x \) | \( \cos x \) |
| \( \cos x \) | \( -\,\sin x \) |
| \( \tan x \) | \( \sec^{2}x \) |
| \( \cot x \) | \( -\,\csc^{2}x \) |
| \( \sec x \) | \( \sec x \tan x \) |
| \( \csc x \) | \( -\,\csc x \cot x \) |
| Inverse Trigonometric Inverse | |
| \( \sin^{-1}x \) | \( \frac{1}{\sqrt{1-x^{2}}} \) |
| \( \cos^{-1}x \) | \( -\,\frac{1}{\sqrt{1-x^{2}}} \) |
| \( \tan^{-1}x \) | \( \frac{1}{1+x^{2}} \) |
| \( \cot^{-1}x \) | \( -\,\frac{1}{1+x^{2}} \) |
| \( \sec^{-1}x \) | \( \frac{1}{\,|x|\,\sqrt{x^{2}-1}} \) |
| \( \csc^{-1}x \) | \( -\,\frac{1}{\,|x|\,\sqrt{x^{2}-1}} \) |
Once you are confident with these formulae, we will start learning how to find derivatives using differentiation techniques — meaning less logic and higher efficiency.
While studying Mathematics, your goal is to learn these techniques properly so that you can apply them in your core subjects whenever required. Only then will your learning become powerful, useful, and meaningful.