derivative of log_{5}(4/(x^2sqrt(1-x)))

Lösung

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

- \frac{- 5 x + 4}{2 ln ( 5 ) x ( - x + 1 )}

Schritte zur Lösung

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

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{4}{x ^{2} 1 - x}) = - \frac{2 ( - 5 x + 4 )}{x ^{3} ( - x + 1 ) - x + 1}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{\frac{4}{x ^{2} 1 - x}} (- \frac{2 ( - 5 x + 4 )}{x ^{3} ( - x + 1 ) - x + 1})

Vereinfache

\frac{1}{ln ( 5 )} \cdot \frac{1}{\frac{4}{x ^{2} 1 - x}} (- \frac{2 ( - 5 x + 4 )}{x ^{3} ( - x + 1 ) - x + 1}) : - \frac{- 5 x + 4}{2 ln ( 5 ) x ( - x + 1 )}

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

\int - 4 x^{2} e^{- 3 x} d x

x \to 1 lim ((f (x)) x^{2} - 2 x)

h \to 0 lim (h^{2} + 5^{h})

\int e^{- 7 x} d x

x \to \infty lim (1 + \frac{3}{x})