Calculus Differentiation Rules

Flashcards covering common calculus differentiation formulas and basic rules from the lecture transcript.

Derivative of a Constant

$$\frac{d}{dx}(c) = 0$$

Derivative of a Constant Multiple

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

Power Rule

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

Product Rule

$$\frac{d}{dx}(u v) = u' v + u v'$$

Quotient Rule

$$\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u' v - u v'}{v^2}$$

Derivative of $e^x$

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

Derivative of $a^x$

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