From 5b61041480ef3df81fad1aa585d33561fb04a2b7 Mon Sep 17 00:00:00 2001 From: arc Date: Sun, 16 Feb 2025 18:37:21 -0700 Subject: [PATCH] vault backup: 2025-02-16 18:37:21 --- education/math/MATH1210 (calc 1)/Derivatives.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index 89c54b0..e22db1e 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -137,7 +137,8 @@ $$ \dfrac{d}{dx} \cot x = -\csc^2 x $$ - 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 -- $\dfrac{d}{dx} y = \dfrac{{dy}{dx} = y'$ +- $\dfrac{d}{dx} y = \dfrac{dy}{dx} = y'$ +- Given the equation $y = x^2$, $\dfrac{d}{dx} y = \dfrac{dy}{dx} = 2x$. # Examples > Differentiate $f(x) = 4\sqrt[3]{x} - \dfrac{1}{x^6}$