(\partial)/(\partial m)((G(m,r)m)/(r^2))

Lösung

\frac{\partial}{\partial m} (\frac{G ( m , r ) m}{r ^{2}})

\frac{1}{r ^{2}} (\frac{\partial}{\partial m} (G (m, r)) m + 1 \cdot G (m, r))

Schritte zur Lösung

\frac{\partial}{\partial m} (\frac{G ( m , r ) m}{r ^{2}})

Behandle

r

als Konstante

Entferne die Konstante:

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

= \frac{1}{r ^{2}} \frac{\partial}{\partial m} (G (m, r) m)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = G (m, r), g = m

= \frac{1}{r ^{2}} (\frac{\partial}{\partial m} (G (m, r)) m + \frac{\partial}{\partial m} (m) G (m, r))

\frac{\partial}{\partial m} (m) = 1

= \frac{1}{r ^{2}} (\frac{\partial}{\partial m} (G (m, r)) m + 1 \cdot G (m, r))

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