Module 6

Partial differentiation

Sol:

2.    

Sol:

3.     Find the value of  n , so that  . satifies the equation

Sol

Further diff wrt

Adding (i) & (ii) we get.

Sol:

5.

Sol:

Again diff wrtx

Detailed Explained of the above step

Again differentiating  x wrt  y

6.

Sol:

Now

Using the formula

Eq (i) becomes.

7.

Sol: Since    treating  y constant

Treating x  constant .................(2)

 Diff again partially wrt x, we get

Now diff (1) partially writ y we get.

8.

Sol:Differentiating x  partiallywrt y get,  .

Differentiating this paritiallywrt x we get.

Diff this again partially wrt y we get

Differentiating    probably

wrt  y

From (i) & (ii)

9.

Sol:

     =

10.

As we want   we

must express  u, v  as function