(\partial)/(\partial y)(e^{-y}(x^2-y^2))

Lösung

\frac{\partial}{\partial y} (e^{- y} (x^{2} - y^{2}))

- e^{- y} (x^{2} - y^{2}) - 2 e^{- y} y

Schritte zur Lösung

\frac{\partial}{\partial y} (e^{- y} (x^{2} - y^{2}))

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = e^{- y}, g = x^{2} - y^{2}

= \frac{\partial}{\partial y} (e^{- y}) (x^{2} - y^{2}) + \frac{\partial}{\partial y} (x^{2} - y^{2}) e^{- y}

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

\frac{\partial}{\partial y} (x^{2} - y^{2}) = - 2 y

= (- e^{- y}) (x^{2} - y^{2}) + (- 2 y) e^{- y}

Vereinfache

= - e^{- y} (x^{2} - y^{2}) - 2 e^{- y} y

\frac{d}{d x} (\frac{1}{14} (e^{7 x} + e^{- 7 x}))

\int_{0}^{1} π (tan (\frac{π}{4} y))^{2} d y

\frac{\partial}{\partial x} (\frac{5 x + 4 y}{3 x + 2 y})

\int (tan (x))^{2} sec (x) d x

\frac{\partial}{\partial x} (6 - x^{3} - y^{5})