Find dy/dx y=x^2e^x

Problem

d()/d(x)*x^2*e^x

Solution

1. Identify the rule needed for differentiation. Since the expression is a product of two functions, u=x^2 and v=e^x use the product rule.

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

3. Differentiate the individual components. The derivative of x^2 is 2*x and the derivative of e^x is e^x

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

d(y)/d(x)=x^2d(e^x)/d(x)+e^xd(x^2)/d(x)

5. Simplify the expression by performing the differentiation and factoring out common terms.

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

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

Final Answer

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

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