Find the Derivative - d/dx y=2xe^x

Problem

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

Solution

1. Identify the rule needed for differentiation. Since the expression 2*x*e^x is a product of two functions, 2*x and e^x the product rule must be applied.

2. Apply the product rule, which states (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x) Let u=2*x and v=e^x

3. Differentiate the individual components. The derivative of u=2*x is (d(2)*x)/d(x)=2 and the derivative of v=e^x is d(e^x)/d(x)=e^x

4. Substitute these values into the product rule formula.

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

5. Simplify the resulting expression by performing the multiplication.

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

6. Factor out the common term 2*e^x to reach the final form.

(d(2)*x*e^x)/d(x)=2*e^x*(x+1)

Final Answer

(d(2)*x*e^x)/d(x)=2*e^x*(x+1)

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