Maths

A set of vocabulary flashcards covering basic derivatives, trigonometric derivatives, the product rule, the quotient rule, and the chain rule from the lecture notes.

$$\sin(kx)$$

Has a derivative of $\frac{dy}{dx} = k\cos(kx)$.

$$\cos(kx)$$

Has a derivative of $\frac{dy}{dx} = -k\sin(kx)$.

$$e^{kx}$$

Has a derivative of $\frac{dy}{dx} = ke^{kx}$.

$$\ln(x)$$

Has a derivative of $\frac{dy}{dx} = \frac{1}{x}$.

$$x^n$$

Has a derivative given by the power rule: $\frac{dy}{dx} = nx^{n-1}$.

$$\tan(x)$$

Has a derivative of $\frac{dy}{dx} = \sec^2(x)$.

$$\operatorname{cosec}(x)$$

Has a derivative of $\frac{dy}{dx} = -\operatorname{cosec}(x)\cot(x)$.

$$\sec(x)$$

Has a derivative of $\frac{dy}{dx} = \sec(x)\tan(x)$.

$$\cot(x)$$

Has a derivative of $\frac{dy}{dx} = -\operatorname{cosec}^2(x)$.

Product Rule ($y = f(x)g(x)$)

The rule for differentiating the product of two functions: $\frac{dy}{dx} = f'(x)g(x) + f(x)g'(x)$.

Quotient Rule ($y = \frac{f(x)}{g(x)}$)

The rule for differentiating the quotient of two functions: $\frac{dy}{dx} = \frac{f'(x)g(x) - f(x)g'(x)}{[g(x)]^2}$.

Chain Rule ($y = f(g(x))$)

The rule for differentiating composite functions: $\frac{dy}{dx} = g'(x)f'(g(x))$, equivalently written as $\frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}$.

Mean =

(Σx) / n

Mean = Σx / n =

Σfx ÷ Σf

Variance σ²

( a² + b² + (-c)² ) ÷ 3f

Theoretical Events P(A) =

n (a) ÷ n(ε)

What does the n(a) mean in n (a) ÷ n(ε)

Number of ways that event can occur

What does the n (ε) mean in n (a) ÷ n(ε)

Total number of ways that events can occur

‘p => q’ means

‘if p then q’

‘p <=> q’ means

‘p if and only q’