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Beliebt Rechnen >

(\partial)/(\partial x)(x^3yz^2+8yz)

Lösung

\frac{\partial}{\partial x} (x^{3} y z^{2} + 8 yz)

Lösung

3 x^{2} y z^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} y z^{2} + 8 yz)

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{3} y z^{2}) + \frac{\partial}{\partial x} (8 yz)

\frac{\partial}{\partial x} (x^{3} y z^{2}) = 3 y z^{2} x^{2}

\frac{\partial}{\partial x} (8 yz) = 0

= 3 y z^{2} x^{2} + 0

Vereinfache

= 3 x^{2} y z^{2}

Beliebte Beispiele

integral of 1/(cos^2(x)+5cos(x)+6)

\int \frac{1}{cos ^{2} ( x ) + 5 cos ( x ) + 6} d x

integral of 10x^3+2x^2+1/2 x+3

\int 10 x^{3} + 2 x^{2} + \frac{1}{2} x + 3 d x

(dy)/(dx)=(y-5)^2

\frac{d y}{d x} = (y - 5)^{2}

\frac{d y}{d x}

derivative (-14x)/(12y)

d er i v a t i v e \frac{- 14 x}{12 y}