Find the Derivative - d/dx f(x)=xsin(x)

Problem

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

Solution

1. Identify the rule needed for the derivative. Since the function is a product of two terms, x and sin(x) the product rule must be used.

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

3. Assign the variables such that u=x and v=sin(x)

4. Differentiate each part individually: d(x)/d(x)=1 and d(sin(x))/d(x)=cos(x)

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

xd(sin(x))/d(x)+sin(x)d(x)/d(x)

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

x*cos(x)+sin(x)⋅1

Final Answer

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

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