Find dy/dx y=xe^x

Problem

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

Solution

1. Identify the function as a product of two terms, u=x and v=e^x which requires the use of 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 each part individually: d(x)/d(x)=1 and d(e^x)/d(x)=e^x

4. Substitute these derivatives back into the product rule formula to get x(e^x)+e(1)^x

5. Factor out the common term e^x to simplify the expression.

Final Answer

d(y)/d(x)=e^x*(x+1)

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