(\partial)/(\partial y)(x(e^y+e^{-y}))

Lösung

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

x (e^{y} - e^{- y})

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{\partial}{\partial y} (e^{y} + e^{- y})

Wende die Summen-/Differenzregel an:

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

= x (\frac{\partial}{\partial y} (e^{y}) + \frac{\partial}{\partial y} (e^{- y}))

\frac{\partial}{\partial y} (e^{y}) = e^{y}

\frac{\partial}{\partial y} (e^{- y}) = - e^{- y}

= x (e^{y} - e^{- y})

\int \frac{- 6 x ^{2}}{( 2 - 2 x ^{3} ) ^{2}} d x

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t an g e n t f (x) = (x^{3} - 16 x)^{10}, (4, 0)

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\int \frac{ln ( u )}{u} d u