(\partial)/(\partial x)(arctan(xy^2))

Lösung

\frac{\partial}{\partial x} (arctan (x y^{2}))

\frac{y ^{2}}{x ^{2} y ^{4} + 1}

Schritte zur Lösung

\frac{\partial}{\partial x} (arctan (x y^{2}))

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{( x y ^{2} ) ^{2} + 1} y^{2} : \frac{y ^{2}}{x ^{2} y ^{4} + 1}

= \frac{y ^{2}}{x ^{2} y ^{4} + 1}

\int \frac{1 - cos ( 2 x )}{2} d x

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

\frac{d}{d x} (\frac{x ^{2}}{( 5 + x )})

\frac{d}{d x} (- x^{2} - 4 x - 2)

\int cosh (0)