   Chapter 16, Problem 22RE

Chapter
Section
Textbook Problem

If f and g are twice differentiable functions, show that ∇2(fg) = f ∇2 g + g∇2 f + 2∇f · ∇g

To determine

To Show: If f and g are twice differentiable functions then 2(fg)=f2g+g2f+2fg .

Explanation

Formula used:

Write the expression for product rule.

(uv)=vu+uv (1)

Write the expression for 2(fg) .

2(fg)=(fg) (2)

Modify equation (2) as follows.

(fg)=gf+fg

Substitute gf+fg for (fg) in equation (2),

2(fg)=[gf

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