Find the Derivative - d/d@VAR f(x)=x+2sin(x)

Problem

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

Solution

1. Identify the function to be differentiated, which is a sum of two terms: x and 2*sin(x)

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives: (d(ƒ)+g)/d(x)=d(ƒ)/d(x)+d(g)/d(x)

3. Differentiate the first term using the power rule: d(x)/d(x)=1

4. Differentiate the second term using the constant multiple rule and the trigonometric derivative rule: (d(2)*sin(x))/d(x)=2*cos(x)

5. Combine the results of the derivatives to find the final expression.

Final Answer

d()/d(x)*(x+2*sin(x))=1+2*cos(x)

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