Consider a function z = xy+x(y^2+1).Find first order partial derivatives, total differential, and total derivative with respect to x.

nagasenaz 2021-02-09 Answered
Consider a function z=xy+x(y2+1).Find first order partial derivatives, total differential, and total derivative with respect to x.
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Expert Answer

Szeteib
Answered 2021-02-10 Author has 102 answers
Step 1
The function is z=xy+x(y2+1)
find the partial derivatives
zx=y+(y2+1)
zx=x+x(2y)
The partial derivatives are:
zx=y+y2+1
zx=x+2xy
Step 2
total differential is given by dz=zxdx+zydy
Substitute the values
dz=(y+y2+1)dx+(x+2xy)dy
The total differential is:
dz=(y+y2+1)dx+(x+2xy)dy
Step 3
The total derivative with respect to x is given by
zx=zx+zyyx
Substitute the values
zx=(y+y2+1)+(x+2xy)dydx
The total derivative with respect to x is:
dzdx=(y+y2+1)+(x+2xy)dydx
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Jeffrey Jordon
Answered 2022-01-30 Author has 2064 answers

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