(\partial)/(\partial x)(e^{-7x}cos(10x))

Lösung

\frac{\partial}{\partial x} (e^{- 7 x} cos (10 x))

- 7 e^{- 7 x} cos (10 x) - 10 e^{- 7 x} sin (10 x)

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{- 7 x} cos (10 x))

Wende die Produktregel an:

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

f = e^{- 7 x}, g = cos (10 x)

= \frac{\partial}{\partial x} (e^{- 7 x}) cos (10 x) + \frac{\partial}{\partial x} (cos (10 x)) e^{- 7 x}

\frac{\partial}{\partial x} (e^{- 7 x}) = - 7 e^{- 7 x}

\frac{\partial}{\partial x} (cos (10 x)) = - sin (10 x) \cdot 10

= (- 7 e^{- 7 x}) cos (10 x) + (- sin (10 x) \cdot 10) e^{- 7 x}

Vereinfache

= - 7 e^{- 7 x} cos (10 x) - 10 e^{- 7 x} sin (10 x)

t an g e n t f (x) = 10 - 4 e^{x}, (0, 6)

\frac{d}{d x} (sin (4))

\frac{d}{d x} (ln (x - 1) + 1)

x \to 2 lim (x ln (\frac{x}{x - 2}))

t an g e n t f (x) = 4 x^{2} + 5 x + 17