From 0e758ef8647ea4130d9e5b938484428a99bbf247 Mon Sep 17 00:00:00 2001 From: arc Date: Tue, 18 Feb 2025 09:36:10 -0700 Subject: [PATCH] vault backup: 2025-02-18 09:36:10 --- education/math/MATH1210 (calc 1)/Derivatives.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index 762ad84..fcc7342 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/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