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

Problem

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

Solution

1. Apply the sum rule for differentiation, which allows the derivative to be taken for each term individually.

d()/d(x)*(x2+y2)=d(x2)/d(x)+d(y2)/d(x)

2. Differentiate the first term with respect to x using the power rule.

d(x2)/d(x)=2*x

3. Differentiate the second term with respect to x using the chain rule (implicit differentiation), since y is assumed to be a function of x

d(y2)/d(x)=2*yd(y)/d(x)

4. Combine the results to find the total derivative of the expression.

2*x+2*yd(y)/d(x)

Final Answer

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

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