Find the Derivative - d/dx x^3e^x

Problem

(d(x3)*ex)/d(x)

Solution

1. Identify the rule needed for the expression, which is a product of two functions: u=x3 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(x3)/d(x)=3*x2 and d(ex)/d(x)=ex

4. Substitute these derivatives back into the product rule formula: x(ex)3+ex*(3*x2)

5. Factor out the common terms x2 and ex to simplify the expression.

Final Answer

(d(x3)*ex)/d(x)=x2*ex*(x+3)

Want more problems? Check here!