derivative of (x^2+4e^{-2x})

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x^{2} + 4) = 2 x

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

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

Vereinfache

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

(x^{2} - 1) (\frac{d y}{d x}) = 2 y

a re a x - y^{2} = 0, x + 2 y^{2} = 3

\frac{\partial}{\partial x} (x^{2} y^{2} z^{2})

t an g e n t f (x) = 7 x + 4, (3, 5)

\frac{d}{d x} (cot^{2} (x) csc (x))