derivative of (x+1/(x^5))

Lösung

\frac{d}{d x} (\frac{x + 1}{x ^{5}})

\frac{- 4 x - 5}{x ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 1}{x ^{5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x + 1 ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( x + 1 )}{( x ^{5} ) ^{2}}

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{1 \cdot x ^{5} - 5 x ^{4} ( x + 1 )}{( x ^{5} ) ^{2}}

Vereinfache

\frac{1 \cdot x ^{5} - 5 x ^{4} ( x + 1 )}{( x ^{5} ) ^{2}} : \frac{- 4 x - 5}{x ^{6}}

= \frac{- 4 x - 5}{x ^{6}}

\frac{\partial}{\partial y} (4 x^{2} y - 5 x y^{2})

d er i v a t i v e \frac{1}{3 x + 1}

d er i v a t i v e f (x) = \frac{( x ^{2} )}{x ^{2} + 9}

\frac{d}{d y} (2 ln (3 x + 4 y))

x \to 0 lim (\frac{4 cos ( x - 4 )}{x})