(\partial)/(\partial t)((3y^2-t^2)/(y^5))

Lösung

\frac{\partial}{\partial t} (\frac{3 y ^{2} - t ^{2}}{y ^{5}})

- \frac{2 t}{y ^{5}}

Schritte zur Lösung

\frac{\partial}{\partial t} (\frac{3 y ^{2} - t ^{2}}{y ^{5}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= \frac{1}{y ^{5}} \frac{\partial}{\partial t} (3 y^{2} - t^{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{y ^{5}} (\frac{\partial}{\partial t} (3 y^{2}) - \frac{\partial}{\partial t} (t^{2}))

\frac{\partial}{\partial t} (3 y^{2}) = 0

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

= \frac{1}{y ^{5}} (0 - 2 t)

Vereinfache

\frac{1}{y ^{5}} (0 - 2 t) : - \frac{2 t}{y ^{5}}

= - \frac{2 t}{y ^{5}}

x \to 0 lim (\frac{( 3 ^{x} - 1 )}{x})

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