(\partial)/(\partial t)(-2sqrt(s^2+t^2))

Lösung

\frac{\partial}{\partial t} (- 2 s^{2} + t^{2})

- \frac{2 t}{s ^{2} + t ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial t} (- 2 s^{2} + t^{2})

Behandle

s

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 \frac{\partial}{\partial t} (s^{2} + t^{2})

Wende die Kettenregel an:

\frac{1}{2 s ^{2} + t ^{2}} \frac{\partial}{\partial t} (s^{2} + t^{2})

= \frac{1}{2 s ^{2} + t ^{2}} \frac{\partial}{\partial t} (s^{2} + t^{2})

\frac{\partial}{\partial t} (s^{2} + t^{2}) = 2 t

= - 2 \cdot \frac{1}{2 s ^{2} + t ^{2}} \cdot 2 t

Vereinfache

- 2 \cdot \frac{1}{2 s ^{2} + t ^{2}} \cdot 2 t : - \frac{2 t}{s ^{2} + t ^{2}}

= - \frac{2 t}{s ^{2} + t ^{2}}

\frac{d}{d x} (6 x + 2)

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f (x) = 3 x

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