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Popular >

derivative of (x^2/(e^x))

Solution

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

Solution

\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}}

Graph

Popular Examples

integral of 13tan^3(x)sec(x)

\int 13 tan^{3} (x) sec (x) d x

(\partial)/(\partial x)(2y-xe^{(xy)})

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

(dy)/(dt)+(3t)/(t^2+1)y=(6t)/(t^2+1)

\frac{d y}{d t} + \frac{3 t}{t ^{2} + 1} y = \frac{6 t}{t ^{2} + 1}

integral of-3x^4

\int - 3 x^{4} d x

derivative of (2x-1/(x+9))

\frac{d}{d x} (\frac{2 x - 1}{x + 9})

Frequently Asked Questions (FAQ)

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