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

Problem

(d(x12)*ex)/d(x)

Solution

1. Identify the rule needed for the derivative of a product of two functions, u(x)=x12 and v(x)=ex

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(x12)/d(x)=12*x11 using the power rule and d(ex)/d(x)=ex

4. Substitute these derivatives back into the product rule formula: x(ex)12+ex*(12*x11)

5. Factor out the common terms x11 and ex to simplify the expression.

Final Answer

(d(x12)*ex)/d(x)=x11*ex*(x+12)

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