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

The derivative of (e^{x^2}/(x^2)) is (2e^{x^2}(x^2-1))/(x^3)

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

The first derivative of (e^{x^2}/(x^2)) is (2e^{x^2}(x^2-1))/(x^3)

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

\frac{2 e ^{x^{2}} ( x ^{2} - 1 )}{x ^{3}}

Solution steps

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

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

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

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

Simplify

\frac{e ^{x^{2}} \cdot 2 x x ^{2} - 2 x e ^{x^{2}}}{( x ^{2} ) ^{2}} : \frac{2 e ^{x^{2}} ( x ^{2} - 1 )}{x ^{3}}

= \frac{2 e ^{x^{2}} ( x ^{2} - 1 )}{x ^{3}}

7 x - x^{2}

\int e^{x} 35 + e^{x} d x

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

\frac{\partial}{\partial x} (ln (1 + \frac{1}{x}))

\frac{\partial}{\partial x} (x^{2} + 2 x y + 3 y^{2})

What is the derivative of (e^{x^2}/(x^2)) ?
The derivative of (e^{x^2}/(x^2)) is (2e^{x^2}(x^2-1))/(x^3)
What is the first derivative of (e^{x^2}/(x^2)) ?
The first derivative of (e^{x^2}/(x^2)) is (2e^{x^2}(x^2-1))/(x^3)