derivative of (3x+1/(sqrt(x+1)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{2}{s ^{2} - 2 s + 9}

y^{^{''}} + 2 y^{^{'}} + y = x^{- 4} e^{- x}

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\int \frac{e ^{x}}{5 e ^{x} + 1} d x