Find the Derivative - d/dx x^9e^x

Problem

d()/d(x)*x9*ex

Solution

1. Identify the rule needed for the expression, which is the product of two functions: u=x9 and v=ex

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

3. Differentiate the individual components: d(x9)/d(x)=9*x8 and d(ex)/d(x)=ex

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

5. Simplify the resulting expression by factoring out the greatest common factor, x8*ex

Final Answer

(d(x9)*ex)/d(x)=x8*ex*(x+9)

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