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Chapter 12: Q 68. (page 965)

Prove that

鈭�(f(x,y)+g(x,y))=鈭�f(x,y)+鈭�g(x,y)

Short Answer

Expert verified

Solve for 鈭�(伪f)=i鈭�(伪f)鈭�x+j鈭�(伪f)鈭�yto prove this.

Step by step solution

01

Given Information

The function is

鈭�(伪f)(x,y)

We need to show that鈭�(伪f)(x,y)=伪鈭�f(x,y).

02

Simplification

Simplifying, we get

鈭�(伪f)=i鈭�(伪f)鈭�x+j鈭�(伪f)鈭�y

鈭�(伪f)=i伪鈭�f鈭�x+j伪鈭�f鈭�y

鈭�(伪f)=伪i鈭�f鈭�x+j鈭�f鈭�y

鈭�(伪f)=伪鈭�f

Hence

鈭�(伪f)=伪鈭�f

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