Second Order Partial Derivatives Problem No.2 - Partial Differentiation - Engineering Mathematics 1

TL;DR

This video explains how to solve a complex numerical problem involving partial differentiation of second order.

Transcript

hello students so after covering the first numerical on partial differentiation of second order let's move to the second numerical so here guys i have a new function and the new question for you and let me tell you that this one is the most difficult question from student point of view because they feel it difficult if they get such type of questio... Read More

Key Insights

• ❓ This numerical problem involves partial differentiation of a function of three variables.
• 🍉 The square term in the function needs to be eliminated before differentiating.
• 😑 The given expression is proved to be equal to a specific value through simplification and substitution.
• 🎗️ The video provides step-by-step explanations and formula reminders to help solve the complex problem.
• ❓ Understanding the derivative formula for logarithmic functions is essential for solving this problem.
• 🎮 The video emphasizes the importance of revising relevant algebraic formulas.
• 🥺 The numerator and denominator terms cancel out using an algebraic formula, leading to the desired result.

Questions & Answers

Q: Why is this numerical problem considered difficult from a student's perspective?

This numerical problem is considered difficult because it involves a square term in the function, requiring additional steps to be taken before partial differentiation can be applied.

Q: How is the square term eliminated before differentiating the function?

The square term is eliminated by expanding it as a bracket squared, using the property that a square term equals the product of the bracket with itself.

Q: What are the values of del u by del x, del u by del y, and del u by del z?

After differentiating the function with respect to x, y, and z, the values of del u by del x, del u by del y, and del u by del z are obtained as 1/(x+y+z), -3/(x+y+z), and -3/(x+y+z) respectively.

Q: How are the values of del u by del x, del u by del y, and del u by del z combined?

The values are combined by adding the corresponding terms in the numerator and taking a common denominator of (x+y+z). This results in a simplified expression of 3/(x+y+z).

Summary & Key Takeaways

• The video introduces a complex numerical problem involving a function of three variables.

• The task is to prove the equality between the given function and a specific expression involving partial differentiation.

• The video explains the step-by-step process of differentiating the function with respect to each variable and simplifying the expression.