What is the derivative of y=(x^2)/(e^x) ?

The derivative of y=(x^2)/(e^x) is (x(2-x))/(e^x)

What is the first derivative of y=(x^2)/(e^x) ?

The first derivative of y=(x^2)/(e^x) is (x(2-x))/(e^x)

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derivative of

y = \frac{x ^{2}}{e ^{x}}

\frac{x ( 2 - x )}{e ^{x}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{e ^{x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} ) e ^{x} - \frac{d}{d x} ( e ^{x} ) x ^{2}}{( e ^{x} ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (e^{x}) = e^{x}

= \frac{2 x e ^{x} - e ^{x} x ^{2}}{( e ^{x} ) ^{2}}

Simplify

\frac{2 x e ^{x} - e ^{x} x ^{2}}{( e ^{x} ) ^{2}} : \frac{x ( 2 - x )}{e ^{x}}

= \frac{x ( 2 - x )}{e ^{x}}

\int \frac{5 x - 2}{x ^{2} - 4} d x

\frac{d}{d x} (sin (8 x + 4))

\frac{d}{d x} ((f (x) (4 x))^{2} + 2)

\frac{d}{d x} (cos (a t))

What is the derivative of y=(x^2)/(e^x) ?
The derivative of y=(x^2)/(e^x) is (x(2-x))/(e^x)
What is the first derivative of y=(x^2)/(e^x) ?
The first derivative of y=(x^2)/(e^x) is (x(2-x))/(e^x)