derivative of (x+1/(sqrt(x^2-3)))

Lösung

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

\frac{- x - 3}{( x ^{2} - 3 ) x ^{2} - 3}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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

\int \frac{1}{( x - 1 ) ( x - 2 )} d x

x \to - 3 lim (\frac{5}{x + 3})

\int (v^{\frac{3}{2}} + \frac{1}{v ^{\frac{3}{2}}}) d v

\int_{1}^{4} (\frac{x}{2} - \frac{5}{x}) d x