(\partial)/(\partial x)((x-3)^2+(y-2)^2)

Lösung

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

2 x - 6

Schritte zur Lösung

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

Vereinfache

(x - 3)^{2} + (y - 2)^{2} : x^{2} - 6 x + y^{2} + 13 - 4 y

= \frac{\partial}{\partial x} (x^{2} - 6 x + y^{2} + 13 - 4 y)

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} (6 x) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (13) - \frac{\partial}{\partial x} (4 y)

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

\frac{\partial}{\partial x} (6 x) = 6

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

\frac{\partial}{\partial x} (13) = 0

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

= 2 x - 6 + 0 + 0 - 0

Vereinfache

= 2 x - 6

in v erse l a pl a ce {\frac{1}{s ^{4} - 9}}

d er i v a t i v e y = 9 e^{x} + \frac{4}{3 x}

d er i v a t i v e - 5 t + 3 + t^{7}

\int_{- 2}^{2} t^{3} (3 + t^{4})^{3} d t

\int (0.3 y^{4} - 8 y^{- 3} + 2) d y