Скачать или смотреть Exercise 5.2 Q.4 | Class 12 | Chapter . 5 Differentiation of vector functions | Class 12 Math

In this lecture, Sir Pharero from Concordia Garden, Karachi explains Exercise 5.2 Question 4 of Chapter 5: Differentiation of Vector Functions for Class 12 Mathematics (Sindh Board). This question focuses on the **derivative of a vector function multiplied by a scalar function**, which is an essential concept in vector calculus and has practical applications in physics, engineering, and mechanics.

We start by reviewing the formula: d/dt [f(t)·r(t)] = f'(t)·r(t) + f(t)·r'(t). I explain each term carefully and demonstrate step-by-step how to differentiate scalar multiples of vector functions. The lecture also covers simplifying results, checking each component, and avoiding common mistakes, such as confusing scalar multiplication with dot or cross product.

Students will also learn the importance of scalar multiplication derivatives in calculating **velocity, acceleration, and motion along a path**. The explanation is in Urdu/Hindi for students across Pakistan, India, Bangladesh, Nepal, and other Urdu/Hindi-speaking regions.

This lecture prepares students for upcoming exercises in vector differentiation, including dot product, cross product, and applications of derivatives in real-life problems.