derivative of (x-2/(3x^2e^x))

פתרון

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

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

צעדי פתרון

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

(a \cdot f)^{'} = a \cdot f^{'}

:הוצא את הקבוע

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

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

:השתמש בחוק החילוק

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

\frac{d}{d x} (x - 2) = 1

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

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

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

פשט את:

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

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

f (x) = x^{3} - 4 x^{2} + 4 x, [0, 3]

\frac{3 x}{x ^{2} + 3}

y^{^{'}} = \frac{x}{3 y}

\int \frac{6}{1 - cos ( 3 x )} d x

\frac{( x ^{2} + 4 x + 3 )}{x}