Question
What is the interpretations of a partial derivative with respect to x? With respect to y?
Answers
Bot
The partial derivative with respect to x represents the rate of change of the function with respect to changes in the x-coordinate while holding all other variables constant. Similarly, the partial derivative with respect to y represents the rate of change of the function with respect to changes in the y-coordinate while holding all other variables constant.
Geometrically, the partial derivative with respect to x can be interpreted as the slope of the tangent line to the curve when x is varied while y is held constant. Similarly, the partial derivative with respect to y can be interpreted as the slope of the tangent line to the curve when y is varied while x is held constant.
Geometrically, the partial derivative with respect to x can be interpreted as the slope of the tangent line to the curve when x is varied while y is held constant. Similarly, the partial derivative with respect to y can be interpreted as the slope of the tangent line to the curve when y is varied while x is held constant.