(\partial)/(\partial x)(6xye^{-x^2-y^2})

Lösung

\frac{\partial}{\partial x} (6 x y e^{- x^{2} - y^{2}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (6 x y e^{- x^{2} - y^{2}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 6 y \frac{\partial}{\partial x} (x e^{- x^{2} - y^{2}})

Wende die Produktregel an:

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

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

= 6 y (\frac{\partial}{\partial x} (x) e^{- x^{2} - y^{2}} + \frac{\partial}{\partial x} (e^{- x^{2} - y^{2}}) x)

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

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

= 6 y (1 \cdot e^{- x^{2} - y^{2}} + (- 2 e^{- x^{2} - y^{2}} x) x)

Vereinfache

6 y (1 \cdot e^{- x^{2} - y^{2}} + (- 2 e^{- x^{2} - y^{2}} x) x) : 6 y (e^{- x^{2} - y^{2}} - 2 e^{- x^{2} - y^{2}} x^{2})

= 6 y (e^{- x^{2} - y^{2}} - 2 e^{- x^{2} - y^{2}} x^{2})

t an g e n t y = 6 sec (x), at x = \frac{π}{6}

\int cos^{4} (d) x d x

x^{2} y^{^{''}} + 3 x y^{^{'}} + 3 y = 0

\frac{\partial}{\partial t} (4 t)

d er i v a t i v e f (x) = 3 x + 8