Find the Derivative - d/d@VAR f(x)=x^2e^x

Problem

d()/d(x)*x2*ex

Solution

1. Identify the rule needed for the derivative of a product of two functions, u(x)=x2 and v(x)=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(x2)/d(x)=2*x and d(ex)/d(x)=ex

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

(d(x2)*ex)/d(x)=x2d(ex)/d(x)+exd(x2)/d(x)

5. Simplify the expression by performing the multiplication.

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

6. Factor out the common term x*ex to reach the final form.

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

Final Answer

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

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