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

Problem

d()/d(x)*x3*ex

Solution

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

2. Apply the product rule, 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(ex)/d(x)=ex

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

x3⋅ex+ex⋅3*x2

5. Factor out the common terms x2 and ex to simplify the expression.

x2*ex*(x+3)

Final Answer

d()/d(x)*x3*ex=x2*ex*(x+3)

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