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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

n \to \infty lim (n^{2} + 2)

\int (\frac{x + 1}{4 x}) d x

y^{2} d y + x^{2} d x = 0

d er i v a t i v e \frac{7}{3} x^{3} (4 x^{5} - 11)^{3}

d er i v a t i v e - 8 x y