Expert Answer to "Find dm differential of m(x,y)=x+y+1"

tintin.superpuma73

Answered question

2022-05-01

Find dm differential of m(x,y)= $\sqrt{x + y + 1}$

Don Sumner

Skilled2023-05-04Added 184 answers

To find the differential of the function

m (x, y) = \sqrt{x + y + 1}

, we need to use the total differential formula, which is given as:

d m = \frac{\partial m}{\partial x} d x + \frac{\partial m}{\partial y} d y

where

d x

and

d y

are the small changes in

x

and

y

, respectively.
First, let's find

\frac{\partial m}{\partial x}

\frac{\partial m}{\partial x} = \frac{1}{2 \sqrt{x + y + 1}} \cdot \frac{\partial}{\partial x} (x + y + 1) = \frac{1}{2 \sqrt{x + y + 1}}

Next, let's find

\frac{\partial m}{\partial y}

\frac{\partial m}{\partial y} = \frac{1}{2 \sqrt{x + y + 1}} \cdot \frac{\partial}{\partial y} (x + y + 1) = \frac{1}{2 \sqrt{x + y + 1}}

Now we can substitute these partial derivatives into the total differential formula:

d m = \frac{1}{2 \sqrt{x + y + 1}} d x + \frac{1}{2 \sqrt{x + y + 1}} d y

Therefore, the differential of

m (x, y) = \sqrt{x + y + 1}

is given by

d m = \frac{1}{2 \sqrt{x + y + 1}} d x + \frac{1}{2 \sqrt{x + y + 1}} d y

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