Explained: "Find the total differetial, given: z=e(x2−y2)"

postillan4

Answered question

2021-09-16

Find the total differetial, given:

z = e^{(x^{2} - y^{2})}

Liyana Mansell

Skilled2021-09-17Added 97 answers

Step 1
Let z=f(x, y) be continuous on an open set S.
Let dx and dy represent changes in x and y, respectively.
Where the partial derivatives

f_{x} and f_{y}

exist, the total differential of z is

d z = f_{x} (x, y) d x + f_{y} (x, y) d y

Step 2
Given,

z = e^{(x^{2} - y^{2})}

We compute the partial derivatives;

f_{x} = 2 x e^{(x^{2} - y^{2})}

f_{y} = - 2 y e^{(x^{2} - y^{2})}

So, the total differential of z;

d z = d_{x} d x + f_{y} d y

d z = 2 x e^{(x^{2} - y^{2})} d x - 2 y e^{(x^{2} - y^{2})} d y

d z = 2 e^{(x^{2} - y^{2})} (x d x - y d y)

d z = 2 e^{(x^{2} - y^{2})} d (x y)

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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