14.5 Notes - f wrt increasing t and therefore depends among...

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Section 14.5 Directional Derivatives and Gradient Vectors Shubhodeep Mukherji 1 Directional Derivatives in the Plane We know that if f ( x,y ) is differentiable, then the rate at which f changes wrt t along a differentiable curve x = g ( t ), y = h ( t ) is df dt = ∂f ∂x dx dt + ∂f ∂y dy dt . At any point P 0 ( x 0 ,y 0 ) = P 0 ( g ( t 0 ) ,h ( t 0 )), this equation gives the rate of change of
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Unformatted text preview: f wrt increasing t and therefore depends, among other things, on the direction of motion along the curve. If the curveis a straight line and t is the arc length parameter along the line measured from P in the direction of a given vector. 1...
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This note was uploaded on 08/03/2011 for the course ECON 101 taught by Professor Profeessor during the Spring '11 term at Aachen University of Applied Sciences.

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