(\partial)/(\partial x)(8x^2+14xy+5y^2)

Lösung

\frac{\partial}{\partial x} (8 x^{2} + 14 x y + 5 y^{2})

16 x + 14 y

Schritte zur Lösung

\frac{\partial}{\partial x} (8 x^{2} + 14 x y + 5 y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (8 x^{2}) + \frac{\partial}{\partial x} (14 x y) + \frac{\partial}{\partial x} (5 y^{2})

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

\frac{\partial}{\partial x} (14 x y) = 14 y

\frac{\partial}{\partial x} (5 y^{2}) = 0

= 16 x + 14 y + 0

Vereinfache

= 16 x + 14 y

t an g e n t x^{2} + y^{2} = 25, (4, 3)

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

\frac{\partial}{\partial x} (5 e^{x y + 4})

y^{^{''}} + 25 y = 2 tan (5 x)

in v erse l a pl a ce \frac{2 s + 5}{s ^{2} + 5 s + 6}