(\partial)/(\partial x)(arctan(y^3x))

Lösung

\frac{\partial}{\partial x} (arctan (y^{3} x))

\frac{y ^{3}}{y ^{6} x ^{2} + 1}

Schritte zur Lösung

\frac{\partial}{\partial x} (arctan (y^{3} x))

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{( y ^{3} x ) ^{2} + 1} y^{3}

Vereinfache

\frac{1}{( y ^{3} x ) ^{2} + 1} y^{3} : \frac{y ^{3}}{y ^{6} x ^{2} + 1}

= \frac{y ^{3}}{y ^{6} x ^{2} + 1}

\int \frac{x}{9 + x ^{2}} d x

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} + 1})

\frac{\partial}{\partial y} (\frac{x ^{2}}{4 - y ^{2}})

\frac{\partial}{\partial p} (\frac{p + q}{p + r})

d er i v a t i v e \frac{1}{d + k e ^{d}}