Find the Derivative - d/dx f(x)=x^2e^x

Problem

(d(x2)*ex)/d(x)

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, x2 and ex use the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Assign the functions for the product rule. Let u=x2 and v=ex

3. Differentiate each part individually. The derivative of x2 is 2*x and the derivative of ex is ex

4. Apply the product rule formula by substituting the functions and their derivatives.

(d(x2)*ex)/d(x)=x2d(ex)/d(x)+exd(x2)/d(x)

5. Substitute the derivatives into the expression.

(d(x2)*ex)/d(x)=x2*ex+ex*(2*x)

6. Simplify the expression by factoring out the common term x*ex

(d(x2)*ex)/d(x)=x*ex*(x+2)

Final Answer

(d(x2)*ex)/d(x)=x2*ex+2*x*ex

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