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Beliebt Rechnen >

d/(dy)(arctan(xy))

Lösung

\frac{d}{d y} (arctan (x y))

Lösung

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

Schritte zur Lösung

\frac{d}{d y} (arctan (x y))

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

\frac{d}{d y} (x y) = x

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

Vereinfache

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

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

Beliebte Beispiele

\int - 15 d x

derivative of xcos(t)

\frac{d}{d x} (x cos (t))

integral of 1/(e^z)

\int \frac{1}{e ^{z}} d z

limit as T approaches 90 of f(T)

T \to 9 0^{\circ} lim (f (T))

(\partial)/(\partial x)(4/3 pix^3)

\frac{\partial}{\partial x} (\frac{4}{3} π x^{3})