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

Problem

d()/d(x)*x^9*e^x

Solution

1. Identify the rule needed for the expression, which is the product of two functions: u=x^9 and v=e^x

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(x^9)/d(x)=9*x^8 and d(e^x)/d(x)=e^x

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

5. Simplify the resulting expression by factoring out the greatest common factor, x^8*e^x

Final Answer

(d(x^9)*e^x)/d(x)=x^8*e^x*(x+9)

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