Define partial derivative of a function of two variables and give its geometrical interpretation.
Understand the Problem
The question is asking for the definition of a partial derivative specifically for a function with two variables, along with an explanation of what this derivative represents geometrically. This involves explaining how the partial derivative relates to the rate of change of the function with respect to one variable while keeping the other variable constant.
Answer
Partial derivative is the slope of the tangent line to a surface at a point in a specific direction.
The final answer is the partial derivative of a function of two variables is the derivative with respect to one variable while keeping the other constant. Its geometrical interpretation is the slope of the tangent line to the surface at a point in a specific direction.
Answer for screen readers
The final answer is the partial derivative of a function of two variables is the derivative with respect to one variable while keeping the other constant. Its geometrical interpretation is the slope of the tangent line to the surface at a point in a specific direction.
More Information
A partial derivative represents how a multivariable function changes as only one of the variables changes, giving a slice of the function surface.
Sources
- Partial Derivatives - UCI Mathematics - math.uci.edu
- Partial Derivative (Definition, Formulas and Examples) - BYJU'S - byjus.com
AI-generated content may contain errors. Please verify critical information
