Find the Derivative - d/dx y=x^10e^x

Problem

d()/d(x)*x10*ex

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, x10 and ex use the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Assign the functions for the product rule. Let u=x10 and v=ex

3. Differentiate each part individually. The derivative of x10 is 10*x9 using the power rule, and the derivative of ex is ex

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

(d(x10)*ex)/d(x)=x10d(ex)/d(x)+exd(x10)/d(x)

5. Substitute the derivatives into the expression.

(d(x10)*ex)/d(x)=x10*ex+ex*(10*x9)

6. Factor out the common terms x9 and ex to simplify the final expression.

(d(x10)*ex)/d(x)=x9*ex*(x+10)

Final Answer

(d(x10)*ex)/d(x)=x9*ex*(x+10)

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