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Popular >

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

Solution

derivative of

\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}}

Popular Examples

integral of arcsin(sqrt(x))sqrt(1-x)

\int arcsin (x) 1 - x d x

limit as r approaches 3 of 4/3 pir^3

r \to 3 lim (\frac{4}{3} π r^{3})

limit as x approaches infinity of (1+3x+2x^3)/(x^3)

x \to \infty lim (\frac{1 + 3 x + 2 x ^{3}}{x ^{3}})

integral of (19)/(x^3-27)

\int \frac{19}{x ^{3} - 27} d x

derivative of (-sin^2(x)/x)

\frac{d}{d x} (\frac{- sin ^{2} ( x )}{x})

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)