Find the Derivative - d/dx x^3e^x

Problem

(d(x^3)*e^x)/d(x)

Solution

1. Identify the rule needed for the expression, which is a product of two functions: u=x^3 and v=e^x

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

3. Differentiate the individual components: d(x^3)/d(x)=3*x^2 and d(e^x)/d(x)=e^x

4. Substitute these derivatives back into the product rule formula: x(e^x)^3+e^x*(3*x^2)

5. Factor out the common terms x^2 and e^x to simplify the expression.

Final Answer

(d(x^3)*e^x)/d(x)=x^2*e^x*(x+3)

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