From 341c388d37b86ca4738a70e588a076c5e106d1f8 Mon Sep 17 00:00:00 2001 From: arc Date: Sun, 16 Feb 2025 18:32:21 -0700 Subject: [PATCH] vault backup: 2025-02-16 18:32:21 --- education/math/MATH1210 (calc 1)/Derivatives.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index 8dfa3bb..89c54b0 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -133,10 +133,11 @@ $$ \dfrac{d}{dx} \csc x = -\csc x \cot x $$ ## Cotangent $$ \dfrac{d}{dx} \cot x = -\csc^2 x $$ -# Implicit Differentiation\ -- $\dfrac{d}{dx} * x^2 = \dfrac{d(x^2)}{dx}$, or, the derivative of $x^2$ with respect to x -- $\dfrac{dx}{dx} = 1$ : The derivative of $x$ with respect to $x$ is one -- +# Implicit Differentiation +- There's a reason differentials are written like a fraction +- $\dfrac{d}{dx} x^2 = \dfrac{d(x^2)}{dx}$, or, "the derivative of $x^2$ with respect to $x$" +- $\dfrac{d}{dx} x = \dfrac{dx}{dx} = 1$ : The derivative of $x$ with respect to $x$ is one +- $\dfrac{d}{dx} y = \dfrac{{dy}{dx} = y'$ # Examples > Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$