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Beliebt Rechnen >

(\partial)/(\partial x)(4z^5+x^4y-y^5x)

Lösung

\frac{\partial}{\partial x} (4 z^{5} + x^{4} y - y^{5} x)

Lösung

- y^{5} + 4 x^{3} y

Schritte zur Lösung

\frac{\partial}{\partial x} (4 z^{5} + x^{4} y - y^{5} x)

Behandle

z, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 z^{5}) + \frac{\partial}{\partial x} (x^{4} y) - \frac{\partial}{\partial x} (y^{5} x)

\frac{\partial}{\partial x} (4 z^{5}) = 0

\frac{\partial}{\partial x} (x^{4} y) = 4 y x^{3}

\frac{\partial}{\partial x} (y^{5} x) = y^{5}

= 0 + 4 y x^{3} - y^{5}

Vereinfache

= - y^{5} + 4 x^{3} y

Beliebte Beispiele

integral of (sin(t)cos(t))

\int (sin (t) cos (t)) d t

limit as x approaches infinity of-4^x

x \to \infty lim (- 4^{x})

integral of 1/((1-u^2)^{3/2)}

\int \frac{1}{( 1 - u ^{2} ) ^{\frac{3}{2}}} d u

integral of 1/(sqrt(1-x))

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

derivative of e^{sin(3x^2})

\frac{d}{d x} (e^{s i n (3 x^{2})})