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Beliebt Rechnen >

(\partial)/(\partial x)(sqrt(x+yz))

Lösung

\frac{\partial}{\partial x} (x + yz)

Lösung

\frac{1}{2 x + yz}

Schritte zur Lösung

\frac{\partial}{\partial x} (x + yz)

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

\frac{1}{2 x + yz} \frac{\partial}{\partial x} (x + yz)

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

\frac{\partial}{\partial x} (x + yz) = 1

= \frac{1}{2 x + yz} \cdot 1

Vereinfache

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

Beliebte Beispiele

integral from 1 to 2 of (13)/(x^3+2x)

\int_{1}^{2} \frac{13}{x ^{3} + 2 x} d x

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

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

(\partial)/(\partial x)(e^{xy}cos(x^2))

\frac{\partial}{\partial x} (e^{x y} cos (x^{2}))

xy^2dy=(y^3-x^3)dx

x y^{2} d y = (y^{3} - x^{3}) d x

d/(dθ)(sqrt(1+sin(2θ)))

\frac{d}{d θ} (1 + sin (2 θ))