- #1
smart_worker
- 131
- 1
Homework Statement
2. The attempt at a solution
By chain rule,
which simpifies to,
After this I am struck.
Multi-variable Calculus : Partial differentiation
- Thread starter smart_worker
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SUMMARY
The discussion focuses on the application of the chain rule in multi-variable calculus, specifically in the context of partial differentiation. The key equation presented is the expression for the partial derivative with respect to a variable \( u \), which incorporates the derivatives of \( x \) and \( y \) with respect to \( u \). The simplification process of this expression is crucial for solving multi-variable calculus problems effectively. Participants emphasize the importance of understanding the relationships between variables when applying the chain rule.
PREREQUISITES- Understanding of multi-variable calculus concepts
- Familiarity with the chain rule in calculus
- Knowledge of partial derivatives
- Basic algebraic manipulation skills
- Study the application of the chain rule in multi-variable calculus
- Explore examples of partial differentiation in various contexts
- Learn about implicit differentiation techniques
- Investigate the geometric interpretation of partial derivatives
Students and educators in mathematics, particularly those focusing on calculus, as well as anyone looking to deepen their understanding of partial differentiation and its applications in multi-variable scenarios.
2. The attempt at a solution
By chain rule,
which simpifies to,
After this I am struck.
- #2
ShayanJ
Science Advisor
- 2,802
- 605
Take into account \frac{\partial}{\partial u}=\frac{\partial x}{\partial u}\frac{\partial}{\partial x} + \frac{\partial y}{\partial u}\frac{\partial}{\partial y} and similarly for v.
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