(\partial)/(\partial x)(-6e^{-3x^2-y^2}x)

Lösung

\frac{\partial}{\partial x} (- 6 e^{- 3 x^{2} - y^{2}} x)

- 6 (- 6 e^{- 3 x^{2} - y^{2}} x^{2} + e^{- 3 x^{2} - y^{2}})

Schritte zur Lösung

\frac{\partial}{\partial x} (- 6 e^{- 3 x^{2} - y^{2}} x)

Behandle

y

als Konstante

Entferne die Konstante:

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

= - 6 \frac{\partial}{\partial x} (e^{- 3 x^{2} - y^{2}} x)

Wende die Produktregel an:

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

f = e^{- 3 x^{2} - y^{2}}, g = x

= - 6 (\frac{\partial}{\partial x} (e^{- 3 x^{2} - y^{2}}) x + \frac{\partial}{\partial x} (x) e^{- 3 x^{2} - y^{2}})

\frac{\partial}{\partial x} (e^{- 3 x^{2} - y^{2}}) = - 6 e^{- 3 x^{2} - y^{2}} x

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

= - 6 ((- 6 e^{- 3 x^{2} - y^{2}} x) x + 1 \cdot e^{- 3 x^{2} - y^{2}})

Vereinfache

- 6 ((- 6 e^{- 3 x^{2} - y^{2}} x) x + 1 \cdot e^{- 3 x^{2} - y^{2}}) : - 6 (- 6 e^{- 3 x^{2} - y^{2}} x^{2} + e^{- 3 x^{2} - y^{2}})

= - 6 (- 6 e^{- 3 x^{2} - y^{2}} x^{2} + e^{- 3 x^{2} - y^{2}})

s l o p e (1 - 2 x) (3 x - 4), at x = 2

f (x) = 2 x^{2} - x + 9

d er i v a t i v e f (x) = 2 - \frac{2}{3} x

\frac{d}{d x} (ln (ln (sec (2 x))))

d er i v a t i v e y = 3 x + \frac{4}{x}