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education/math/MATH1210 (calc 1)/Derivatives.md

@@ -81,6 +81,13 @@ Then break into two different fractions:
 
 $$\lim_{h \to 0} \dfrac{f(x + h)}{1} * \dfrac{(g(x + h) - g(x))}{h)} + \dfrac{g(x)}{1} *\dfrac{f(x + h) - f(x)}{h} $$
 From here, you can take the limit of each fraction, therefore showing that to find the derivative of two values multiplied together, you can use the formula:
-$$ \dfrac{d}{dx}(f(x) * g(x)) = f(x) * g'(x) + f'(x) $$
+$$ \dfrac{d}{dx}(f(x) * g(x)) = f(x) * g'(x) + f'(x)*g(x) $$
-# Natural Exponential Function
+
-$$ \dfrac{d}{dx} e^x = e^x $$
+# Constant Multiple Rule
+$$ \dfrac{d}{dx}[c*f(x)] = c * f'(x) $$
+# Quotient Rule
+$$ \dfrac{d}{dx}(\dfrac{f(x)}{g(x)}) = \dfrac{f'(x)g(x) -f(x)g'(x)}{(g(x))^2}  $$
+
+# Exponential Rule
+$$ \dfrac{d}{dx} e^x = e^x $$
+$$ \dfrac{d}{dx}a^x