What is the derivative of (e^{xx}-e^x/(x^2)) ?

The derivative of (e^{xx}-e^x/(x^2)) is (x(2e^{x^2}x-e^x)-2(-e^x+e^{x^2}))/(x^3)

What is the first derivative of (e^{xx}-e^x/(x^2)) ?

The first derivative of (e^{xx}-e^x/(x^2)) is (x(2e^{x^2}x-e^x)-2(-e^x+e^{x^2}))/(x^3)

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Popular >

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

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

Solution steps

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

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

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

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

Simplify

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

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

x \to 5 lim (\frac{6}{x})

\int \frac{1}{1 + tan ( x )} d x

y^{^{''}} + 6 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

\int x \cdot e^{- 3 x} d x

\int \frac{x ^{2} + 6 x + 5}{x ^{2} + 2 x + 1} d x

What is the derivative of (e^{xx}-e^x/(x^2)) ?
The derivative of (e^{xx}-e^x/(x^2)) is (x(2e^{x^2}x-e^x)-2(-e^x+e^{x^2}))/(x^3)
What is the first derivative of (e^{xx}-e^x/(x^2)) ?
The first derivative of (e^{xx}-e^x/(x^2)) is (x(2e^{x^2}x-e^x)-2(-e^x+e^{x^2}))/(x^3)