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

Problem

d()/d(x)*2*x*ex

Solution

1. Identify the rule needed for differentiation. Since the expression 2*x*ex is a product of two functions, 2*x and ex 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=ex

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

4. Substitute these values into the product rule formula.

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

5. Simplify the resulting expression by performing the multiplication.

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

6. Factor out the common term 2*ex to reach the final form.

(d(2)*x*ex)/d(x)=2*ex*(x+1)

Final Answer

(d(2)*x*ex)/d(x)=2*ex*(x+1)

Want more problems? Check here!