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Beliebt Rechnen >

(\partial)/(\partial x)(arctan(xsqrt(y)))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

integral of 2cos^2(x)

\int 2 cos^{2} (x) d x

derivative of sqrt(cos(e^{x^2cos(x))})

\frac{d}{d x} (cos (e^{x^{2} c o s (x)}))

sum from n=1 to infinity of (4^n)/(5^n)

n = 1 \sum \infty \frac{4 ^{n}}{5 ^{n}}

derivative sqrt(8t^2-t)

d er i v a t i v e 8 t^{2} - t

derivative (3x+5)^2

d er i v a t i v e (3 x + 5)^{2}