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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

\frac{\partial}{\partial x} (3 yz) = 0

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

Vereinfache

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

Beliebte Beispiele

tangent f(x)=(x^3-7)(3x^2+5)

t an g e n t f (x) = (x^{3} - 7) (3 x^{2} + 5)

x^{^{'}} = a x + b

integral of xe^{(-x)/4}

\int x e^{\frac{- x}{4}} d x

derivative of (x^5-4x^2/(x^3))

\frac{d}{d x} (\frac{x ^{5} - 4 x ^{2}}{x ^{3}})

f(x)=cos((ln(x+1))^2-e^{x^2})

f (x) = cos ((ln (x + 1))^{2} - e^{x^{2}})