Anonymous

高等微積分有關偏微分!幫幫忙謝謝

Suppose that the function f:R^n ->R is continuously differentiable.Let x be a point in R^n. For p a nonzero point in R^n and α a nonzero

real number. show that δf/[δ(αP)] (x) = α[δf/δP](x)

Update:

I can't understand

thank you

Rating

This can be done by chain rule

let $$u=ap$$ and $$f=f(u)$$ at u=x
then $$\frac{\partial f}{\partial p}(x)=\frac{\partial f}{\partial u}(x)\cdot \frac{\partial u}{\partial p}=a\frac{\partial f}{\partial ap}(x)$$