(\partial)/(\partial x)(ln(x^6+y^3))

Lösung

\frac{\partial}{\partial x} (ln (x^{6} + y^{3}))

\frac{6 x ^{5}}{x ^{6} + y ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (x^{6} + y^{3}))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{x ^{6} + y ^{3}} \frac{\partial}{\partial x} (x^{6} + y^{3})

= \frac{1}{x ^{6} + y ^{3}} \frac{\partial}{\partial x} (x^{6} + y^{3})

\frac{\partial}{\partial x} (x^{6} + y^{3}) = 6 x^{5}

= \frac{1}{x ^{6} + y ^{3}} \cdot 6 x^{5}

Vereinfache

\frac{1}{x ^{6} + y ^{3}} \cdot 6 x^{5} : \frac{6 x ^{5}}{x ^{6} + y ^{3}}

= \frac{6 x ^{5}}{x ^{6} + y ^{3}}

t a y l or sin (x) \frac{π}{4}

\int sec^{2} (11 x) d x

l a pl a ce t r an s f or m e^{- 9 t}

t an g e n t y = 3 + 6 x + 8 x e^{x}

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