derivative ln(((8x-9)^2)/(-x-1))

Lösung

ableitung von

ln (\frac{( 8 x - 9 ) ^{2}}{- x - 1})

- \frac{8 x + 25}{( 8 x - 9 ) ( - x - 1 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{( 8 x - 9 ) ^{2}}{- x - 1}))

Wende die Kettenregel an:

\frac{1}{\frac{( 8 x - 9 ) ^{2}}{- x - 1}} \frac{d}{d x} (\frac{( 8 x - 9 ) ^{2}}{- x - 1})

= \frac{1}{\frac{( 8 x - 9 ) ^{2}}{- x - 1}} \frac{d}{d x} (\frac{( 8 x - 9 ) ^{2}}{- x - 1})

\frac{d}{d x} (\frac{( 8 x - 9 ) ^{2}}{- x - 1}) = \frac{- 64 x ^{2} - 128 x + 225}{( - x - 1 ) ^{2}}

= \frac{1}{\frac{( 8 x - 9 ) ^{2}}{- x - 1}} \cdot \frac{- 64 x ^{2} - 128 x + 225}{( - x - 1 ) ^{2}}

Vereinfache

\frac{1}{\frac{( 8 x - 9 ) ^{2}}{- x - 1}} \cdot \frac{- 64 x ^{2} - 128 x + 225}{( - x - 1 ) ^{2}} : - \frac{8 x + 25}{( 8 x - 9 ) ( - x - 1 )}

= - \frac{8 x + 25}{( 8 x - 9 ) ( - x - 1 )}

d er i v a t i v e x^{\frac{11}{2}}

x^{^{'}} = - x^{2}

d er i v a t i v e f (2) = 3 x^{2} - 2 x + 5

\int \frac{x + 2}{x ^{3}} d x

\frac{\partial}{\partial x} (2 x e^{x^{2}})