derivative of ln(x^8y)

Lösung

\frac{d}{d x} (ln (x^{8} y))

\frac{8 y + x \frac{d y}{d x}}{x y}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{8} y))

Wende die Kettenregel an:

\frac{1}{x ^{8} y} \frac{d}{d x} (x^{8} y)

= \frac{1}{x ^{8} y} \frac{d}{d x} (x^{8} y)

\frac{d}{d x} (x^{8} y) = 8 x^{7} y + \frac{d y}{d x} x^{8}

= \frac{1}{x ^{8} y} (8 x^{7} y + \frac{d y}{d x} x^{8})

Vereinfache

\frac{1}{x ^{8} y} (8 x^{7} y + \frac{d y}{d x} x^{8}) : \frac{8 y + x \frac{d y}{d x}}{x y}

= \frac{8 y + x \frac{d y}{d x}}{x y}

\int_{0}^{1} x e^{5 x} d x

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 - 8 t - (18 t e^{2 t} + 2 e^{2 t})

\int 2 \cdot x \cdot ln (x) d x

\frac{\partial}{\partial y} (- \frac{1}{2} x - 3 y + 1)

\int u cos (u) d u