(\partial)/(\partial x)(x^3+8x^2y+12y^2)

Lösung

\frac{\partial}{\partial x} (x^{3} + 8 x^{2} y + 12 y^{2})

3 x^{2} + 16 x y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} + 8 x^{2} y + 12 y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (8 x^{2} y) + \frac{\partial}{\partial x} (12 y^{2})

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

\frac{\partial}{\partial x} (8 x^{2} y) = 16 y x

\frac{\partial}{\partial x} (12 y^{2}) = 0

= 3 x^{2} + 16 y x + 0

Vereinfache

= 3 x^{2} + 16 x y

\frac{d y}{d x} + 8 y = e^{7 x}

\frac{d}{d x} (e^{x} (11 x^{2} - 22 x + 22))

im pl i c i t \frac{d y}{d x}, y^{4} = 4 x y

x \to 0 lim (\frac{e ^{3 x} - 1}{2 x})

\frac{d}{d y} (\frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{2}})