derivative of (7x^2+3x+7/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{7 x ^{2} + 3 x + 7}{x})

\frac{21 x ^{2} + 3 x - 7}{2 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x ^{2} + 3 x + 7}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 7 x ^{2} + 3 x + 7 ) x - \frac{d}{d x} ( x ) ( 7 x ^{2} + 3 x + 7 )}{( x ) ^{2}}

\frac{d}{d x} (7 x^{2} + 3 x + 7) = 14 x + 3

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

= \frac{( 14 x + 3 ) x - \frac{1}{2 x} ( 7 x ^{2} + 3 x + 7 )}{( x ) ^{2}}

Vereinfache

\frac{( 14 x + 3 ) x - \frac{1}{2 x} ( 7 x ^{2} + 3 x + 7 )}{( x ) ^{2}} : \frac{21 x ^{2} + 3 x - 7}{2 x x}

= \frac{21 x ^{2} + 3 x - 7}{2 x x}

x \to 0 + lim (7 (\frac{1}{x} - cot (x)))

d er i v a t i v e y = x^{x}

x \to + π + lim (csc (x))

\frac{d}{d x} ((x - 42)^{2} - 3 x ln ((x - 100)^{2}))

(e^{x} y) d y = (e^{- y} + e^{- 2 x - y}) d x