derivative of ((x+1^3)/(x^{3/2)})

Lösung

\frac{d}{d x} (\frac{( x + 1 ) ^{3}}{x ^{\frac{3}{2}}})

\frac{3 ( x + 1 ) ^{2} ( x - 1 )}{2 x ^{\frac{5}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x + 1 ) ^{3}}{x ^{\frac{3}{2}}})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{3 ( x + 1 ) ^{2} x ^{\frac{3}{2}} - \frac{3 x ^{\frac{1}{2}}}{2} ( x + 1 ) ^{3}}{( x ^{\frac{3}{2}} ) ^{2}} : \frac{3 ( x + 1 ) ^{2} ( x - 1 )}{2 x ^{\frac{5}{2}}}

= \frac{3 ( x + 1 ) ^{2} ( x - 1 )}{2 x ^{\frac{5}{2}}}

t an g e n t f (x) = 4 x - x^{2}, at x = 1

x \to - 2 - lim (\frac{x ^{2} - 4}{x + 2})

\int x x^{2} - 2 d x

x \to 0 lim (\frac{π}{x})

t an g e n t f (x) = x x^{2} + 21