Best solutions to - "Find the total differential z=5x3y2"

College
Calculus and Analysis
Differential Calculus
Derivatives

tabita57i

Answered question

2021-09-29

Find the total differential

z = 5 x^{3} y^{2}

Answer & Explanation

coffentw

Skilled2021-09-30Added 103 answers

Step 1
The given function is $z = 5 x^{3} y^{2}$
Total differential:
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 $d z = f_{x} (x, y) d x + f_{y} (x, y) d y$ .
The partial derivative is,
$f_{x} = 15 x^{2} y^{2}$
$f_{y} = 10 x^{3} y$
Step 2
The total differential of z is,
$d z = f_{x} (x, y) d x + f_{y} (x, y) d y$ .
$= 15 x^{2} y^{2} d x + 10 x^{3} y d y$

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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