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Question Number 163028 by BHOOPENDRA last updated on 03/Jan/22

Answered by aleks041103 last updated on 03/Jan/22

$$\frac{df}{dn}=\hat{n}.grad\left(f\right)=\frac{n_x}{\mid n\mid }\frac{\partial f}{\partial x}+\frac{n_y}{\mid n\mid }\frac{\partial f}{\partial y}+\frac{n_z}{\mid n\mid }\frac{\partial f}{\partial z}=$$$$=\frac{2}{\sqrt{17}}\frac{\partial f}{\partial x}+\frac{2}{\sqrt{17}}\frac{\partial f}{\partial y}+\frac{3}{\sqrt{17}}\frac{\partial f}{\partial z}=$$$$=\frac{2}{\sqrt{17}}24x^2\sqrt{y}z+\frac{2}{\sqrt{17}}\frac{2x^{3}z}{\sqrt{y}}+\frac{3}{\sqrt{17}}4x^3\sqrt{y}$$

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