(\partial)/(\partial x)(sqrt(xy^2+y^2))

Lösung

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

\frac{y}{2 x + 1}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{1}^{3} 2 r^{4} ln (r) d r

s l o p e (- 4, - 4), (2, 5)

\int (4 x - 3) (2 x - 1) d x

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

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