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Beliebt Rechnen >

(\partial)/(\partial x)(y+3xz+x^3)

Lösung

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

Lösung

3 x^{2} + 3 z

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (y) = 0

\frac{\partial}{\partial x} (3 x z) = 3 z

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

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

Vereinfache

= 3 x^{2} + 3 z

Beliebte Beispiele

tangent f(x)=x^3-4x^2-9x+11

t an g e n t f (x) = x^{3} - 4 x^{2} - 9 x + 11

integral from-infinity to infinity of x^2e^{(-x^2)/2}

\int_{- \infty}^{\infty} x^{2} e^{\frac{- x ^{2}}{2}} d x

implicit (dy)/(dx),xy+4e^y=4e

im pl i c i t \frac{d y}{d x}, x y + 4 e^{y} = 4 e

integral of x^2(x^3+5)^{10}

\int x^{2} (x^{3} + 5)^{10} d x

y^{''}+2y^'+y=3-e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = 3 - e^{- t}