Find dy/dx y=xe^x

Problem

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

Solution

1. Identify the function as a product of two terms, u=x and v=ex 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(ex)/d(x)=ex

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

5. Factor out the common term ex to simplify the expression.

Final Answer

d(y)/d(x)=ex*(x+1)

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