Find the Derivative - d/dx (x^2)/(e^x)

Problem

d()/d(x)(x^2)/(e^x)

Solution

1. Identify the rule needed for the derivative of a quotient of two functions, which is the quotient rule.

2. Apply the formula for the quotient rule, d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v^2) where u=x^2 and v=e^x

3. Differentiate the numerator u to get d(x^2)/d(x)=2*x

4. Differentiate the denominator v to get d(e^x)/d(x)=e^x

5. Substitute these derivatives into the quotient rule formula.

(e^x*(2*x)−x(e^x)^2)/((e^x)^2)

6. Factor out the common term e^x from the numerator.

(e^x*(2*x−x^2))/((e^x)^2)

7. Simplify the expression by canceling one e^x from the numerator and denominator.

(2*x−x^2)/(e^x)

Final Answer

d()/d(x)(x^2)/(e^x)=(2*x−x^2)/(e^x)

Want more problems? Check here!