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Beliebt Rechnen >

(\partial)/(\partial x)((x+2)^2-2(y-1)^2-5)

Lösung

\frac{\partial}{\partial x} ((x + 2)^{2} - 2 (y - 1)^{2} - 5)

Lösung

2 x + 4

Schritte zur Lösung

\frac{\partial}{\partial x} ((x + 2)^{2} - 2 (y - 1)^{2} - 5)

Vereinfache

(x + 2)^{2} - 2 (y - 1)^{2} - 5 : x^{2} + 4 x + 4 y - 2 y^{2} - 3

= \frac{\partial}{\partial x} (x^{2} + 4 x + 4 y - 2 y^{2} - 3)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (4 y) - \frac{\partial}{\partial x} (2 y^{2}) - \frac{\partial}{\partial x} (3)

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

\frac{\partial}{\partial x} (4 x) = 4

\frac{\partial}{\partial x} (4 y) = 0

\frac{\partial}{\partial x} (2 y^{2}) = 0

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

= 2 x + 4 + 0 - 0 - 0

Vereinfache

= 2 x + 4

Beliebte Beispiele

y^{''}+4y^'+3y=x

y^{^{''}} + 4 y^{^{'}} + 3 y = x

tangent f(x)=sqrt(x+5),\at x=11

t an g e n t f (x) = x + 5, at x = 11

tangent sqrt(3x-5)

t an g e n t 3 x - 5

integral of 1/(sqrt(x))e^{-sqrt(x)}

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

derivative of (x+1/x (x-1/x))

\frac{d}{d x} ((x + \frac{1}{x}) (x - \frac{1}{x}))