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

nagasenaz

nagasenaz

Answered question

2021-02-09

Consider a function z=xy+x(y2+1).Find first order partial derivatives, total differential, and total derivative with respect to x.

Answer & Explanation

Szeteib

Szeteib

Skilled2021-02-10Added 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
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-30Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?