Calculating Differential – Exercise 4233


Find the differential of the function

p=\ln \sqrt{x^2+y^2}

Final Answer



We will find the function differential with the differential formula

dp=p'_x dx+p'_y dy

In the formula above we see the function partial derivatives. Hence, we calculate them.

p'_x(x,y)=\frac{1}{\sqrt{x^2+y^2}}\cdot \frac{1}{2\sqrt{x^2+y^2}}\cdot 2x=


p'_y(x,y)=\frac{1}{\sqrt{x^2+y^2}}\cdot \frac{1}{2\sqrt{x^2+y^2}}\cdot 2y=


Now, we put the derivatives in the formula and get

dp=p'_x dx+p'_y dy


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