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

Lösung

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

\frac{5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

\int (x^{4} + x^{2} + x) d x

\frac{\partial}{\partial x} (x^{8})

t an g e n t y = \frac{1}{2 + 3 x}, (2, \frac{1}{8})

\frac{d}{d x} (\frac{4}{x ^{2} + 1})

x \to 0 lim (\frac{1}{2 x} - \frac{1}{e ^{2 x} - 1})