derivative of ln(((1-x)/((x+5)^3)))

Lösung

\frac{d}{d x} (ln (\frac{( 1 - x )}{( x + 5 ) ^{3}}))

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

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{( 1 - x )}{( x + 5 ) ^{3}}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (cos (\frac{π x}{2}))

\frac{\partial}{\partial x} (6 x + 12)

t an g e n t f (x) = \frac{8}{7 x}, at 1, 87

\frac{\partial}{\partial x} (x^{6} - 4 x^{2} y^{4} + 3 y^{2})

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