derivative of (5+3x-6sqrt(x)/x)

Lösung

\frac{d}{d x} (\frac{5 + 3 x - 6 x}{x})

\frac{3 x - 5}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 + 3 x - 6 x}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 5 + 3 x - 6 x ) x - \frac{d x}{d x} ( 5 + 3 x - 6 x )}{x ^{2}}

\frac{d}{d x} (5 + 3 x - 6 x) = - \frac{3}{x} + 3

\frac{d x}{d x} = 1

= \frac{( - \frac{3}{x} + 3 ) x - 1 \cdot ( 5 + 3 x - 6 x )}{x ^{2}}

Vereinfache

\frac{( - \frac{3}{x} + 3 ) x - 1 \cdot ( 5 + 3 x - 6 x )}{x ^{2}} : \frac{3 x - 5}{x ^{2}}

= \frac{3 x - 5}{x ^{2}}

(- 4 x + 3 y - 7) d x - (x + 1) d y = 0

\frac{\partial}{\partial x} (x + x y^{2})

\int \frac{1}{sin ( x )} \frac{cos ( x )}{sin ( x )} d x

h \to 0 lim (\frac{( 1 + h ) 3 - 1}{h})

x, y \to (0, 0) lim (\frac{( 2 x ^{2} y )}{x ^{2} + y ^{4}})