(\partial)/(\partial x)(x^2+y^2-y^2x-7)

Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} - y^{2} x - 7)

2 x - y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} - y^{2} x - 7)

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} (y^{2}) - \frac{\partial}{\partial x} (y^{2} x) - \frac{\partial}{\partial x} (7)

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

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

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

\frac{\partial}{\partial x} (7) = 0

= 2 x + 0 - y^{2} - 0

Vereinfache

= 2 x - y^{2}

t an g e n t f (x) = x^{2} - 2, (3, 7)

x \to 0 lim ((c e^{x} + 1) i f)

\int \frac{x ^{2} + 3}{x + 1} d x

\frac{d}{d x} (\frac{x ^{4}}{4} + \frac{1}{8 x ^{2}})

\int_{0}^{2} x^{2} ln (x) d x