Find dy/dx y=x^9e^x

Problem

d()/d(x)*x^9*e^x

Solution

1. Identify the rule needed for differentiation. Since the expression is a product of two functions, x^9 and e^x use the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Assign the functions to variables. Let u=x^9 and v=e^x

3. Differentiate each part separately.

d(x^9)/d(x)=9*x^8

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

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

d(y)/d(x)=x^9d(e^x)/d(x)+e^xd(x^9)/d(x)

d(y)/d(x)=x^9*e^x+e^x*(9*x^8)

5. Simplify the expression by factoring out the greatest common factor, which is x^8*e^x

d(y)/d(x)=x^8*e^x*(x+9)

Final Answer

d(y)/d(x)=x^8*e^x*(x+9)

Want more problems? Check here!