Find the Derivative - d/dX x^2e^(3x)

Problem

d()/d(x)*x2*e(3*x)

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, x2 and e(3*x) use the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Assign the functions for the product rule. Let u=x2 and v=e(3*x)

3. Differentiate each part individually.

d(x2)/d(x)=2*x

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

4. Apply the product rule formula by substituting the parts.

d()/d(x)*x2*e(3*x)=x2*(3*e(3*x))+e(3*x)*(2*x)

5. Simplify the expression by factoring out common terms, such as x and e(3*x)

d()/d(x)*x2*e(3*x)=3*x2*e(3*x)+2*x*e(3*x)

d()/d(x)*x2*e(3*x)=x*e(3*x)*(3*x+2)

Final Answer

d()/d(x)*x2*e(3*x)=x*e(3*x)*(3*x+2)

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