Find the Derivative - d/dx 2x+y

Problem

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

Solution

1. Apply the sum rule for differentiation, which states that the derivative of a sum is the sum of the derivatives.

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

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

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

3. Differentiate the second term with respect to x using implicit differentiation, treating y as a function of x

d(y)/d(x)=d(y)/d(x)

4. Combine the results to find the final expression for the derivative.

2+d(y)/d(x)

Final Answer

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

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