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Question Number 188017 by Rupesh123 last updated on 24/Feb/23

Answered by aleks041103 last updated on 24/Feb/23

$$f(x,y)=ln(x^2+y^2)=2ln\left(r\right)$$$$r=\sqrt{x^2+y^2}$$$$\Rightarrow f(x,y)=f\left(r\right)$$$$\Rightarrow ▽f=\frac{2}{r}\overrightarrow{e_r}$$$$\Rightarrow maxrateofchange=\frac{2}{r}=\frac{2}{\sqrt{4^2+{(-3)}^2}}=\frac{2}{5}$$$$direction=\overrightarrow{e_r}=(\frac{4}{5},\frac{-3}{5})$$$$\Rightarrow Ans:$$$$Maxrateofchange=0.4=\frac{2}{5}$$$$Direction=(0.8,-0.6)=\frac{1}{5}(4,-3)$$

Commented by Rupesh123 last updated on 24/Feb/23

Perfect ��

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