Find the Derivative - d/dx y=x^5e^x

Problem

d()/d(x)*x5*ex

Solution

1. Identify the rule needed for the expression, which is the product of two functions: u=x5 and v=ex

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

3. Differentiate the individual components: d(x5)/d(x)=5*x4 and d(ex)/d(x)=ex

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

x5d(ex)/d(x)+exd(x5)/d(x)

5. Simplify the resulting expression by performing the multiplication.

x5*ex+5*x4*ex

6. Factor out the common terms x4 and ex to reach the final form.

x4*ex*(x+5)

Final Answer

(d(x5)*ex)/d(x)=x4*ex*(x+5)

Want more problems? Check here!