Prior Knowledge: https://youtu.be/XvA7mR3RW5o https://youtu.be/ablVVBy-21E https://youtu.be/VtcAXsy_QKQ https://youtu.be/9pyF71bgKY4 Key Concepts: 00:00 Overview of Sketching Rational Functions 01:18 A Checklist for Sketching Rational Functions 08:50 Sketching Reciprocal Functions 12:37 Application of Sketching Rational Functions

**The polynomials in a rational function can have complex/imaginary coefficients** Exploring Stationary Points: https://youtu.be/ablVVBy-21E

Tutoring Enquiries: contact@wyneducation.com **The x-axis is cut off on the last problem :-| ... you get the idea! Prior Knowledge https://youtu.be/uK10FwKGtcM?si=B_pvZ-kQL1BbQvVm https://youtu.be/IppKqgbu19A?si=Gi_Z83w3QZi19Y3m https://youtu.be/RIn7am4KhCU https://youtu.be/VtcAXsy_QKQ?si=w8qxetG60kzQBPOO https://youtu.be/QJ5xQRLhNqI Key Concepts 00:00 Overview 01:24 Relating Rates of Change for a Square Based Pyramid 07:07 Related Rates of Change Problem 09:38 Related Rates of Change for Parametric Equations 13:21 Related Rates of Change for Parametric as a Composition 16:24 Related Rate of Change for Parametric Equations Problem

Tutoring Enquiries: contact@wyneducation.com Prior Knowledge https://youtu.be/VtcAXsy_QKQ https://www.youtube.com/playlist?list=PLB46vjmEuCC0OQrIkSV0HDNKbGQTRisN- Key Concepts: 00:00 Overview 00:38 The Second Derivative Explained 03:01 Concavity & Points of Inflection 07:02 Classifying Points Through Derivative Analysis

Prior Knowledge: https://youtu.be/FwGRZQXwXUQ?si=LnTRynrmHoX3UaTB https://youtu.be/TeKZMTgKjEg?si=kc6Ox-iaWBIGLMdm https://youtu.be/VtcAXsy_QKQ?si=7_u8y_s5xj8j3e7L https://youtu.be/uK10FwKGtcM?si=b-uDy5lKsX5xKzeq https://youtu.be/O9V4sUx0QFE?si=yFIh5Oyq0McgDt_K https://youtu.be/QJ5xQRLhNqI?si=SoBoKsp_HLv8nAqf 00:00 Overview of Derivatives of Inverse Circular Functions 01:00 Derivative of Inverse Sine Visualised 03:35 Derivative of Inverse Cosine Visualised 04:35 Derivative of Inverse Tangent Visualised 05:30 Proof(s) of Inverse Cosine Derivative 08:20 Inverse Sine Function Derivative 10:17 Inverse Cosine Function Derivative 11:31 Inverse Tangent Function Derivative 12:55 Inverse Circular Function Derivative Application

Complementary Info: https://youtu.be/uK10FwKGtcM https://youtu.be/VtcAXsy_QKQ https://youtu.be/TeKZMTgKjEg

Prior Knowledge: https://youtu.be/VtcAXsy_QKQ?si=YkFvhz8_8UVWtFwU https://youtu.be/Gx4LqNFo6bY?si=rgMephc13tU-r7b- https://youtu.be/zQrdqsnzONQ?si=n9r4zqtK8oyy_eIj https://youtu.be/Gym2ed8TSGQ?si=muzI6D1mkfylH7j6 https://youtu.be/hxZoOwtdVcU?si=2UkgtKvyI1o1qiZH 00:00 Overview of Inverse Function Differentiation 01:07 Inverse Function Differentiation Explained 04:08 Application Problem

00:00 Overview of Differentiation for Specialist Maths 3&4 01:31 The Big Picture of Differentiation 05:00 The Product Rule Explained 07:17 The Quotient Rule Explained 09:20 The Chain Rule Explained 12:11 Proof of the Derivative of tan(kx) 16:26 The Derivative of log_|x| Additional Resources Differentiation by First Principles: https://youtu.be/PdP4jLZoitY Proof of the Product Rule: https://youtu.be/xYqo212tqzQ Chain Rule: https://youtu.be/htLXt61SOvc More Detail on the Derivative of log_e|x|: https://youtu.be/KJVH9ogzoto Circular Functions Explained: https://youtu.be/FwGRZQXwXUQ Reciprocal Circular Functions: https://youtu.be/z6CY-hpug0o