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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

integral of 1/(sqrt(1+x^2))

\int \frac{1}{1 + x ^{2}} d x

derivative y=sin(arccos(t))

d er i v a t i v e y = sin (arccos (t))

derivative of (15/(x^2))

\frac{d}{d x} (\frac{15}{x ^{2}})

integral from 0 to 12 of 1/(36-x^2)

\int_{0}^{12} \frac{1}{36 - x ^{2}} d x

integral from 0 to pi/6 of tsin(2t)

\int_{0}^{\frac{π}{6}} t sin (2 t) d t