Lesson 5: Power rule, Product rule, Quoteint rule

you have learned may rules like: $$\frac{d}{dx} c = 0$$ $$\frac{d}{dx} c \cdot f(x) = c \cdot \frac{d}{dx} f(x)$$ but there are some mor important rules:

1. The Power Rule

this is the easiest rule in all of calculus: $$\frac{d}{dx} x^n = nx^{n-1}$$ for example: $$\frac{d}{dx} x^2 = 2x$$

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2. The Product Rule

$$\frac{d}{dx} f(x) \cdot g(x) = f'(x) \cdot g(x) + f(x) \cdot g'(x)$$ (btw \(f'(x)\) is the same as the derivative and \(f''(x)\) is the second derivative... and so on) for example: $$\frac{d}{dx} x^2 \cdot 3x^3 = 2x \cdot 3x^3 + x^2 \cdot 9x^2$$

3. The Quotient Rule

$$\frac{d}{dx} \frac{f(x)}{g(x)} = \frac{f'(x) \cdot g(x) - f(x) \cdot g'(x)}{[g(x)]^2}$$ for example: $$\frac{d}{dx} \frac{x}{5x^2} = \frac{1 \cdot 5x^2 - x \cdot 10x}{[5x^2]^2}$$

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