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We explore 12 derivative exercises and 12 integral exercises using Sympy, visualized in Jupyter Notebook.\n\n## 📋 Table of Contents  \n1. [Installation](#installation)  \n2. [Usage](#usage)  \n3. [Exercises](#exercises)  \n   - [Derivatives](#derivatives)  \n   - [Integrals](#integrals)  \n4. [Tech Stack](#tech-stack)  \n5. [Contributing](#contributing)  \n6. [License](#license)\n\n## ⚙️ Installation  \n```bash\n# 1. Clone the repo  \ngit clone https://github.com/your-username/your-repo.git  \ncd your-repo  \n\n# 2. Create \u0026 activate virtual environment  \npython3 -m venv venv  \nsource venv/bin/activate          # macOS/Linux  \n# venv\\Scripts\\Activate.ps1       # Windows PowerShell  \n\n# 3. Install dependencies  \npip install -r requirements.txt  \n\n# Launch Jupyter Notebook  \njupyter notebook calculus_project.ipynb\n\nWork through the Derivatives section first, then Integrals.\n\nCode cells render results in framed LaTeX for clarity.\n\n## ▶️ Usage\n\n* Ensure your virtual environment is activated\n\n* Launch the notebook:\n\njupyter notebook calculus_project.ipynb\n\nComplete the Derivatives section first, then Integrals\n\nEach code cell displays the result as a framed LaTeX equation for clarity\n\n## 🧮 Exercises\n\n📈 Derivatives\n\nPower rule, product rule, quotient rule, chain rule\n\n12 worked examples:\n\n1. x**3 - 5*x**2 + 2*x - 1\n\n2. sin(x)*exp(x)\n\n3. log(x)/x\n\n4. cos(x)**2\n\n5. exp(-2*x)\n\n6. tan(x)\n\n7. sqrt(x)\n\n8. (3*x+1)**5\n\n9. x**x\n\n10. atan(x)\n\n11. sin(x**2)\n\n12. log(x,10)\n\n📉 Integrals\n\nPower integrals, trigonometric identities, substitution, integration by parts\n\n12 worked examples:\n\n1. ∫ x^3 dx\n\n2. ∫ 1/(x^2+1) dx\n\n3. ∫ sin^2(x) dx\n\n4. ∫ x*exp(x) dx\n\n5. ∫ exp(-2*x) dx\n\n6. ∫ log(x) dx\n\n7. ∫ cos(x) dx\n\n8. ∫ tan(x) dx\n\n9. ∫ x^2*cos(x) dx\n\n10. ∫ 2*x/(x^2+1) dx\n\n11. ∫ sin(3*x) dx\n\n12. ∫₀^∞ exp(-x) dx\n\n🧰 Tech Stack\n\n* Python 3.8+\n\n* Sympy for symbolic math\n\n* NumPy \u0026 Matplotlib for numerical checks \u0026 plots\n\n* Jupyter Notebook for interactive presentation\n\n🤝 Contributing\n* Fork the repository\n\n* Create a new branch\n\ngit checkout -b feature/your-feature\n\n* Commit your changes\n\ngit commit -m \"Add some feature\"\n\ngit commit -m \"Add some feature\"\n\n* Push to your branch\n\ngit push origin feature/your-feature\n\n* Open a Pull Request\n\n👉🏽 Please follow the existing style and update documentation as needed.\n\n📜 License\n @ This project is licensed under the MIT License. See LICENSE for details.\n\n\n\n\n\n\n\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdataspieler12345%2Fmathematics_for_ai","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdataspieler12345%2Fmathematics_for_ai","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdataspieler12345%2Fmathematics_for_ai/lists"}