4_(Total)_[Compatibility_Mode].pdf - Multivariable Calculus Module \u2013 3 Lecture Class-4(Total Derivative By Dr Hemant Kumar Nashine Department of

4_(Total)_[Compatibility_Mode].pdf - Multivariable Calculus...

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Multivariable Calculus Module – 3 Lecture Class-4 ( Total Derivative ) By Dr Hemant Kumar Nashine Department of Mathematics, SAS, VIT Vellore
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Total Derivative If u = f(x, y) , where x = ϕ (t) and y = ψ (t) , then we can express u as a function of t alone by substituting the values of x and y in f(x, y) . Thus we can find the ordinary derivative du/dt which is called the total derivative of u to distinguish it from the partial derivatives ∂u/ ∂ x and u/ y . 08-Sep-18 Dr Hemant K Nashine, Professor 2
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To find du/dt without actually substituting the values of x and y in f(x,y) , we use following Chain rule : Taking t = x , (i) becomes, 08-Sep-18 Dr Hemant K Nashine, Professor 3
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08-Sep-18 Dr Hemant K Nashine, Professor 4
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