derivative f(x)=(x^2+9)/(sqrt(x))

Lösung

ableitung von

f (x) = \frac{x ^{2} + 9}{x}

\frac{3 x ^{2} - 9}{2 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 9}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 9 ) x - \frac{d}{d x} ( x ) ( x ^{2} + 9 )}{( x ) ^{2}}

\frac{d}{d x} (x^{2} + 9) = 2 x

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

= \frac{2 x x - \frac{1}{2 x} ( x ^{2} + 9 )}{( x ) ^{2}}

Vereinfache

\frac{2 x x - \frac{1}{2 x} ( x ^{2} + 9 )}{( x ) ^{2}} : \frac{3 x ^{2} - 9}{2 x x}

= \frac{3 x ^{2} - 9}{2 x x}

\int 3 csc^{2} (t) - 5 sec (t) tan (t) d t

x \to 8 - lim (\frac{1}{( x - 8 ) ^{2}})

\int x e^{2 x + 1} d x

x \to 0 lim (\frac{x}{x ^{2} - 6 x})

t an g e n t f (x) = \frac{5 x - 7}{x + 1}, at x = 0