Find the Derivative - d/dx x^12e^x

Problem

(d(x^12)*e^x)/d(x)

Solution

1. Identify the rule needed for the derivative of a product of two functions, u(x)=x^12 and v(x)=e^x

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

3. Differentiate the individual components: d(x^12)/d(x)=12*x^11 using the power rule and d(e^x)/d(x)=e^x

4. Substitute these derivatives back into the product rule formula: x(e^x)^12+e^x*(12*x^11)

5. Factor out the common terms x^11 and e^x to simplify the expression.

Final Answer

(d(x^12)*e^x)/d(x)=x^11*e^x*(x+12)

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