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

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

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

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

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

\frac{1 - 2 x ^{2}}{e ^{x^{2}}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

= \frac{1 - 2 x ^{2}}{e ^{x^{2}}}

\int \frac{x ^{2}}{( 1 + x ^{2} ) ^{2}} d x

\int sin^{4} (x co) s^{3} x d x

\int (4 x - 2) d x

\frac{d}{d x} (- \frac{sin ( ln ( x ) )}{x})

x^{2} y^{^{'}} + 4 x y - y^{3} = 0

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