Find the Derivative - d/dx y=x^4e^x

Problem

d()/d(x)*x4*ex

Solution

1. Identify the rule needed for the expression, which is a product of two functions: u=x4 and v=ex

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

3. Differentiate each part individually: d(x4)/d(x)=4*x3 and d(ex)/d(x)=ex

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

d(y)/d(x)=x4d(ex)/d(x)+exd(x4)/d(x)

5. Simplify the resulting expression by performing the multiplication.

d(y)/d(x)=x4*ex+4*x3*ex

6. Factor out the common terms x3 and ex to reach the final form.

d(y)/d(x)=x3*ex*(x+4)

Final Answer

d()/d(x)*x4*ex=x3*ex*(x+4)

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