Find the Derivative - d/d@VAR f(x)=x^3sin(x)

Problem

d()/d(x)*x3*sin(x)

Solution

1. Identify the rule needed for the expression, which is a product of two functions: u(x)=x3 and v(x)=sin(x)

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

3. Differentiate the individual components: d(x3)/d(x)=3*x2 and d(sin(x))/d(x)=cos(x)

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

5. Simplify the resulting expression by organizing the terms.

Final Answer

(d(x3)*sin(x))/d(x)=x3*cos(x)+3*x2*sin(x)

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