Find the Derivative - d/dx xsin(x)

Problem

d()/d(x)*x*sin(x)

Solution

1. Identify the rule needed for the expression, which is a product of two functions: u=x and v=sin(x)

2. Apply the product rule formula, which states (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

3. Differentiate the individual components: d(x)/d(x)=1 and d(sin(x))/d(x)=cos(x)

4. Substitute these derivatives back into the product rule formula.

5. Simplify the resulting expression to find the final derivative.

Final Answer

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

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