Find the Derivative - d/dx natural log of x^2+y^2

Problem

d(ln(x2+y2))/d(x)

Solution

1. Identify the rule required for the derivative of a natural logarithm, which is d(ln(u))/d(x)=1/u⋅d(u)/d(x)

2. Apply the chain rule by setting u=x2+y2 and finding the derivative of the inner function with respect to x

3. Differentiate the inner terms, treating y as a function of x (implicit differentiation), which gives d(x2+y2)/d(x)=2*x+2*yd(y)/d(x)

4. Combine the results into a single expression by multiplying the reciprocal of the inner function by its derivative.

Final Answer

d(ln(x2+y2))/d(x)=(2*x+2*yd(y)/d(x))/(x2+y2)

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