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

Lösung

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

1 + 2 e^{- 2 y x^{2}} x^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= 1 - (- 2 x^{2} e^{- 2 x^{2} y})

Vereinfache

= 1 + 2 e^{- 2 y x^{2}} x^{2}

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

\int_{0}^{0.1} x arctan (2 x) d x

\int 14 cot^{4} (x) d x

\int \frac{2}{e ^{3 x}} d x

\frac{d}{d x} (4^{s i n (2) (x) + c o s (3 x)})