Assume that all the given functions are differentiable. If z = f ( x , y ) , where x = r cos θ and y = r sin θ , (a) find ∂ z / ∂ r and ∂ z / ∂ θ and (b) show that ( ∂ z ∂ x ) 2 + ( ∂ z ∂ y ) 2 = ( ∂ z ∂ r ) 2 + 1 r 2 ( ∂ z ∂ θ ) 2
Assume that all the given functions are differentiable. If z = f ( x , y ) , where x = r cos θ and y = r sin θ , (a) find ∂ z / ∂ r and ∂ z / ∂ θ and (b) show that ( ∂ z ∂ x ) 2 + ( ∂ z ∂ y ) 2 = ( ∂ z ∂ r ) 2 + 1 r 2 ( ∂ z ∂ θ ) 2
Solution Summary: The author explains that all functions are differentiable by applying chain rule.
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY