(\partial)/(\partial x)((x+y^2)*e^{-4x+2y})

Lösung

\frac{\partial}{\partial x} ((x + y^{2}) \cdot e^{- 4 x + 2 y})

e^{- 4 x + 2 y} - 4 e^{- 4 x + 2 y} (x + y^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} ((x + y^{2}) e^{- 4 x + 2 y})

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x + y^{2}, g = e^{- 4 x + 2 y}

= \frac{\partial}{\partial x} (x + y^{2}) e^{- 4 x + 2 y} + \frac{\partial}{\partial x} (e^{- 4 x + 2 y}) (x + y^{2})

\frac{\partial}{\partial x} (x + y^{2}) = 1

\frac{\partial}{\partial x} (e^{- 4 x + 2 y}) = - 4 e^{- 4 x + 2 y}

= 1 \cdot e^{- 4 x + 2 y} + (- 4 e^{- 4 x + 2 y}) (x + y^{2})

Vereinfache

= e^{- 4 x + 2 y} - 4 e^{- 4 x + 2 y} (x + y^{2})

im pl i c i t \frac{d y}{d x}, y = (9 + x)^{\frac{1}{x}}

x \to 5 lim ((34 - x^{2}) x)

\int (e^{- x} - e^{2}) (e^{x} + e^{- 5}) d x

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

\int 2 x ln (x) d x