Find the Derivative - d/dx y=xcos(x)

Problem

d()/d(x)*x*cos(x)

Solution

1. Identify the function as a product of two terms, u=x and v=cos(x) which requires the use of the product rule.

2. Recall the product rule formula for differentiation: (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(cos(x))/d(x)=−sin(x)

4. Substitute these components into the product rule formula: x*(−sin(x))+cos(x)*(1)

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

Final Answer

(d(x)*cos(x))/d(x)=cos(x)−x*sin(x)

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