(\partial)/(\partial x)((x-3)^2+(y-4)^2)

Lösung

\frac{\partial}{\partial x} ((x - 3)^{2} + (y - 4)^{2})

2 x - 6

Schritte zur Lösung

\frac{\partial}{\partial x} ((x - 3)^{2} + (y - 4)^{2})

Vereinfache

(x - 3)^{2} + (y - 4)^{2} : x^{2} - 6 x + y^{2} + 25 - 8 y

= \frac{\partial}{\partial x} (x^{2} - 6 x + y^{2} + 25 - 8 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} (25) - \frac{\partial}{\partial x} (8 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} (25) = 0

\frac{\partial}{\partial x} (8 y) = 0

= 2 x - 6 + 0 + 0 - 0

Vereinfache

= 2 x - 6

\frac{d}{d x} (2 sin (2 cos (x)))

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

\int (- g t + V) d t

\int e^{9 x} cos (5 x) d x

d er i v a t i v e y = - x^{3} + 2 x