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

@@ -122,7 +122,15 @@ $$ \dfrac{d}{dx}(\dfrac{f(x)}{g(x)}) = \dfrac{f'(x)g(x) -f(x)g'(x)}{(g(x))^2}  $
 $$ \dfrac{d}{dx} e^x = e^x $$
 $$ \dfrac{d}{dx}a^x = a^x*(\ln(a)) $$
 for all $a > 0$
+# Logarithms
 
+For natural logarithms:
+$$ \dfrac{d}{dx} \ln |x| = \dfrac{1}{x} $$
+
+For other logarithms:
+$$ \dfrac{d}{dx} \log_a x = \dfrac{1}{(\ln a) x}$$
+When solving problems that make use of logarithms, consider making use of logarithmic properties to make life easier, eg:
+$$ \ln(\dfrac{x}{y}) = \ln(x) - \ln(y) $$
 # Chain Rule
 $$ \dfrac{d}{dx} f(g(x)) = f'(g(x))*g'(x) $$
 ## Examples