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Beliebt Rechnen >

(\partial)/(\partial x)(x^2y^3-1)

Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} - 1)

Lösung

2 x y^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} - 1)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2} y^{3}) - \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (1) = 0

= 2 y^{3} x - 0

Vereinfache

= 2 x y^{3}

Beliebte Beispiele

derivative 4e^{x+2}+e^{-3}

d er i v a t i v e 4 e^{x + 2} + e^{- 3}

xy^'+y=y^2,y(1)=-15

x y^{^{'}} + y = y^{2}, y (1) = - 15

fläche y=28-x^2,y=3x,y= 3/5 x

a re a y = 28 - x^{2}, y = 3 x, y = \frac{3}{5} x

integral of (16/2 x^3+12x^5-2x+1)

\int (\frac{16}{2} x^{3} + 12 x^{5} - 2 x + 1) d x

derivative f(x)=5e^x(cos(x)-sin(x))

d er i v a t i v e f (x) = 5 e^{x} (cos (x) - sin (x))