Find the Derivative - d/dx x^8e^x

Problem

d()/d(x)*x8*ex

Solution

1. Identify the rule needed for the derivative. Since the expression x8*ex is a product of two functions, x8 and ex the product rule must be used.

2. Apply the product rule formula, which states that d()/d(x)*u*v=ud(v)/d(x)+vd(u)/d(x) Let u=x8 and v=ex

3. Differentiate the individual components. The derivative of x8 is 8*x7 using the power rule, and the derivative of ex is ex

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

(d(x8)*ex)/d(x)=x8d(ex)/d(x)+exd(x8)/d(x)

5. Simplify the resulting expression by performing the differentiation and factoring if possible.

(d(x8)*ex)/d(x)=x8*ex+ex*(8*x7)

6. Factor out the common terms x7 and ex to reach the final form.

(d(x8)*ex)/d(x)=x7*ex*(x+8)

Final Answer

(d(x8)*ex)/d(x)=x8*ex+8*x7*ex

Want more problems? Check here!