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Beliebt Rechnen >

(\partial)/(\partial x)((x^3-y^2)^2)

Lösung

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

Lösung

6 x^{2} (x^{3} - y^{2})

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= 2 (x^{3} - y^{2}) \cdot 3 x^{2}

Vereinfache

= 6 x^{2} (x^{3} - y^{2})

Beliebte Beispiele

(\partial)/(\partial x)((x+y)^5)

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

fläche y=1-x^2,y=x-1

a re a y = 1 - x^{2}, y = x - 1

integral from-1 to 3 of (-x)^3

\int_{- 1}^{3} (- x)^{3} d x

derivative of (-2x+y/(-x+2y))

\frac{d}{d x} (\frac{- 2 x + y}{- x + 2 y})

implicit (dy)/(dx),2xy=5

im pl i c i t \frac{d y}{d x}, 2 x y = 5