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Popular >

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

Solution

derivative of

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

Solution

\frac{e ^{x} ( x - 2 )}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}} : \frac{e ^{x} ( x - 2 )}{x ^{3}}

= \frac{e ^{x} ( x - 2 )}{x ^{3}}

Popular Examples

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\int - sin^{2} (x) cos (x) d x

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\frac{d}{d x} (\frac{x + 3}{x})

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\frac{d}{d x} (5^{(6 x^{2} - 7 x) (8 x^{2} + 9)})

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\int - 2 x + 9 x^{2} - 4 x^{3} + 16 d x

Frequently Asked Questions (FAQ)

What is the derivative of y=(e^x)/(x^2) ?
The derivative of y=(e^x)/(x^2) is (e^x(x-2))/(x^3)
What is the first derivative of y=(e^x)/(x^2) ?
The first derivative of y=(e^x)/(x^2) is (e^x(x-2))/(x^3)