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Problem Metadata

Date: November 16, 2025

Problem Number: #6

Problem Curator: @Phanie

lymphoidcell - Overview

Indonesian version: TBA

Unit Tangent Vector of a Parametric Curve in $R^3$

Category: Machine Learning Math - Linear Algebra

Difficulty Level: Beginner - Intermediate

Prerequisites:

• Differentiation of elementary functions
• Vector-valued functions and componentwise derivaties
• Euclidean norm in $R^3$

Also check this out: Supplementary Problems for DAY 6

Problem Statement

Consider the curve

$$ G(t) = (e^t, \sin t, t^2) \subset R^3 $$

(a) Compute the derivative