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

The derivative of (e^{x^2}/(x^3)) is (e^{x^2}(2x^2-3))/(x^4)

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

The first derivative of (e^{x^2}/(x^3)) is (e^{x^2}(2x^2-3))/(x^4)

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

\frac{e ^{x^{2}} ( 2 x ^{2} - 3 )}{x ^{4}}

Solution steps

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

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

Simplify

\frac{e ^{x^{2}} \cdot 2 x x ^{3} - 3 x ^{2} e ^{x^{2}}}{( x ^{3} ) ^{2}} : \frac{e ^{x^{2}} ( 2 x ^{2} - 3 )}{x ^{4}}

= \frac{e ^{x^{2}} ( 2 x ^{2} - 3 )}{x ^{4}}

2 (x - 1)

\int e^{2 y - y^{2}} d y

x \to 3 lim (x - x)

3 \frac{d y}{d x} = \frac{e ^{y} sin ^{2} ( x )}{y sec ( x )}

\int \frac{x + 1}{( x ^{2} + 4 x + 5 ) ^{2}} d x

What is the derivative of (e^{x^2}/(x^3)) ?
The derivative of (e^{x^2}/(x^3)) is (e^{x^2}(2x^2-3))/(x^4)
What is the first derivative of (e^{x^2}/(x^3)) ?
The first derivative of (e^{x^2}/(x^3)) is (e^{x^2}(2x^2-3))/(x^4)