(\partial)/(\partial x)(ln(x^7+y^4))

Lösung

\frac{\partial}{\partial x} (ln (x^{7} + y^{4}))

\frac{7 x ^{6}}{x ^{7} + y ^{4}}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (x^{7} + y^{4}))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{x ^{7} + y ^{4}} \frac{\partial}{\partial x} (x^{7} + y^{4})

= \frac{1}{x ^{7} + y ^{4}} \frac{\partial}{\partial x} (x^{7} + y^{4})

\frac{\partial}{\partial x} (x^{7} + y^{4}) = 7 x^{6}

= \frac{1}{x ^{7} + y ^{4}} \cdot 7 x^{6}

Vereinfache

\frac{1}{x ^{7} + y ^{4}} \cdot 7 x^{6} : \frac{7 x ^{6}}{x ^{7} + y ^{4}}

= \frac{7 x ^{6}}{x ^{7} + y ^{4}}

in v erse l a pl a ce \frac{2}{s ^{3}}

\int_{0}^{\frac{π}{2}} - 2 cos^{5} (x) d x

d er i v a t i v e (6 z + e^{- z^{2}})^{3}

\frac{\partial}{\partial x} (2 y sin (10 x - y))

(\frac{x ^{2}}{2 x + 4})^{^{'}}