Um, if r of t is equal to t, square I plus e raised to t, j minus 2, cos pi t k. Find Derivative of Vector Functions |MAT102 | Module 1| S2 |KTU Part 2 ** Vector Calculus Differentiation** Finding the first derivative of a vector function: Given a vector function , its derivative is: Differentiate each component separately. Example 1: Example 2: Use product rule for the j component. Example 3: Example 4: Finding the second derivative of a vector function: Find the first derivative, then differentiate each component again. Example with specific point evaluation: Find the derivative at a specific value of (e.g., ). Substitute the value into the derivative expression. Example involving trigonometric functions: Remember trigonometric identities and values (e.g., , ). Likely Exam Questions: Find the first and second derivatives of a given vector function. Evaluate the derivative of a vector function at a specific point. Solve problems involving vector functions and their derivatives that include trigonometric and exponential functions. Apply the product rule and chain rule to vector functions. Final Recap: Remember to differentiate each component of the vector function separately. Pay close attention to the rules of differentiation (product rule, chain rule) and trigonometric identities. Practice evaluating the derivatives at specific points. Points here