Higher Secondary Calculus - Differentiation Rules

A set of flashcards covering the fundamental differentiation rules and formulas for polynomials, exponentials, and trigonometric functions as presented in the lecture notes.

$$\frac{d}{dx}(x^n)$$

$$nx^{n-1}$$

$$\frac{d}{dx}(c)$$

$$0$$

$$\frac{d}{dx}(x)$$

$$1$$

$$\frac{d}{dx}(2\sqrt{x})$$

$$\frac{1}{\sqrt{x}}$$

$$\frac{d}{dx}(e^x)$$

$$e^x$$

$$\frac{d}{dx}(a^x)$$

$$a^x \ln(a)$$

$$\frac{d}{dx}(\ln(x))$$

$$\frac{1}{x}$$

$$\frac{d}{dx}(uv)$$

$$u \frac{dv}{dx} + v \frac{du}{dx}$$

$$\frac{d}{dx}(\frac{1}{x^n})$$

$$\frac{-n}{x^{n+1}}$$

$$\frac{d}{dx}(\sin(x))$$

$$\cos(x)$$

$$\frac{d}{dx}(\cos(x))$$

$$-\sin(x)$$

$$\frac{d}{dx}(\tan(x))$$

$$\sec^2(x)$$

$$\frac{d}{dx}(\cot(x))$$

$$-\csc^2(x)$$

$$\frac{d}{dx}(\sec(x))$$

$$\sec(x) \tan(x)$$

$$\frac{d}{dx}(\csc(x))$$

$$-\csc(x) \cot(x)$$

$$\frac{d}{dx}(\sin^{-1} x)$$

$$\frac{1}{\sqrt{1-x^2}}$$