Find the Derivative - d/dx 5xe^x

Problem

(d(5)*x*ex)/d(x)

Solution

1. Identify the rule needed for differentiation. Since the expression 5*x*ex is a product of two functions, 5*x and ex the product rule must be applied.

2. Apply the product rule, which states that (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x) Let u=5*x and v=ex

3. Differentiate the individual components.

(d(5)*x)/d(x)=5

d(ex)/d(x)=ex

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

(d(5)*x*ex)/d(x)=5*x⋅ex+ex⋅5

5. Simplify the expression by factoring out the common term 5*ex

(d(5)*x*ex)/d(x)=5*ex*(x+1)

Final Answer

(d(5)*x*ex)/d(x)=5*ex*(x+1)

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