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

Problem

d()/d(x)*x9*ex

Solution

1. Identify the rule needed for differentiation. Since the expression is a product of two functions, x9 and ex 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=x9 and v=ex

3. Differentiate each part separately.

d(x9)/d(x)=9*x8

d(ex)/d(x)=ex

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

d(y)/d(x)=x9d(ex)/d(x)+exd(x9)/d(x)

d(y)/d(x)=x9*ex+ex*(9*x8)

5. Simplify the expression by factoring out the greatest common factor, which is x8*ex

d(y)/d(x)=x8*ex*(x+9)

Final Answer

d(y)/d(x)=x8*ex*(x+9)

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