derivative of ((sqrt(x)+1^2)/(sqrt(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

a re a y = x^{3}, y = 2 x^{2}

\int 8 x^{3} - 9 x^{2} + 4 d x

\int (8 x + 3)^{4} d x

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

a re a (48 - 2 x) - x, [- 8, 24]