Let f(x)=(x^(2))/(e^(x)). f^(')(x)=

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Let  f(x)=(x^(2))/(e^(x)).  f^(')(x)=

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Quotient Rule Explanation: To find the derivative of the function f(x) = (x^2)/(e^x), we will use the quotient rule. The quotient rule states that if we have a function that is the quotient of two functions, u(x)/v(x), then its derivative is given by (u'(x)v(x) - u(x)v'(x))/(v(x))^2. Here, u(x) = x^2 and v(x) = e^x.Derivative of u(x): First, we need to find the derivative of u(x) = x^2. The derivative of x^2 with respect to x is 2x.Derivative of v(x): Next, we need to find the derivative of v(x) = e^x. The derivative of e^x with respect to x is e^x.Applying Quotient Rule: Now we apply the quotient rule. The derivative of f(x) is given by (u'(x)v(x) - u(x)v'(x))/(v(x))^2. Substituting u'(x) = 2x, v(x) = e^x, and v'(x) = e^x, we get:  f'(x) = (2x * e^x - x^2 * e^x) / (e^x)^2.Simplifying Expression: We can simplify the expression by factoring out e^x from the numerator and canceling out one e^x from the numerator and denominator:  f'(x) = (e^x(2x - x^2)) / e^(2x).Final Derivative: After canceling out e^x, we get:  f'(x) = (2x - x^2) / e^x.

Let $f(x)=\frac{x^{2}}{e^{x}}$ . $\newline$ $f^{\prime}(x)=$

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