(\partial)/(\partial x)(x^2+8xy+17y^2-2y+1)

Lösung

\frac{\partial}{\partial x} (x^{2} + 8 x y + 17 y^{2} - 2 y + 1)

2 x + 8 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + 8 x y + 17 y^{2} - 2 y + 1)

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} (8 x y) + \frac{\partial}{\partial x} (17 y^{2}) - \frac{\partial}{\partial x} (2 y) + \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (8 x y) = 8 y

\frac{\partial}{\partial x} (17 y^{2}) = 0

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

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

= 2 x + 8 y + 0 - 0 + 0

Vereinfache

= 2 x + 8 y

\frac{\partial}{\partial x} (sin (2 t))

\int (- 8 x^{7} y^{- 5} + 6 x^{6} y^{- 4}) d y

\int_{1}^{t} \frac{31}{x ^{3}} d x

x \to 0 lim (\frac{ln ^{2} ( x )}{x})

\int sec^{2} (t) + t (t^{2} + 1)^{3} + t^{2} ln (t) d t