From 7d7efe3d552bf1856a251203c139e5823b4f8cb0 Mon Sep 17 00:00:00 2001 From: arc Date: Thu, 30 Jan 2025 08:58:43 -0700 Subject: [PATCH] vault backup: 2025-01-30 08:58:43 --- education/math/MATH1210 (calc 1)/Derivatives.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1210 (calc 1)/Derivatives.md b/education/math/MATH1210 (calc 1)/Derivatives.md index 8825a7f..7158737 100644 --- a/education/math/MATH1210 (calc 1)/Derivatives.md +++ b/education/math/MATH1210 (calc 1)/Derivatives.md @@ -35,4 +35,8 @@ Given the equation $y = f(x)$, the following are all notations used to represent - If the slope of the tangent line is vertical # Higher Order Differentials -- Take the differential of a differential \ No newline at end of file +- Take the differential of a differential + +Using the definition of a derivative to determine the derivative of $f(x) = x^n$, where $n$ is any natural number. + +$$ f'(x) = \lim_{h \to 0} \dfrac{(x + h)^n - x^n}{h} $$