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

Lösung

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

\frac{6}{x}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{6}{x}

\frac{d y}{d x} + \frac{y}{x} = 8 x^{5} y^{2}

\int_{0}^{6} \frac{8 t}{( t - 7 ) ^{2}} d t

\frac{\partial}{\partial x} (\frac{z ( x + y )}{x + y + z})

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

x \to - 10 lim (- (\frac{1}{x + 10}))