Find dy/dx y=x^6e^x

Problem

d()/d(x)*x^6*e^x

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, x^6 and e^x use the product rule.

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

3. Assign the variables such that u=x^6 and v=e^x

4. Differentiate each part individually.

d(x^6)/d(x)=6*x^5

d(e^x)/d(x)=e^x

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

d(y)/d(x)=x^6*e^x+e^x*(6*x^5)

6. Factor out the common terms x^5 and e^x to simplify the expression.

d(y)/d(x)=x^5*e^x*(x+6)

Final Answer

d(y)/d(x)=x^6*e^x+6*x^5*e^x

Want more problems? Check here!