derivative f(x)=2e^x(cos(x)-sin(x))

Lösung

ableitung von

f (x) = 2 e^{x} (cos (x) - sin (x))

- 4 e^{x} sin (x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (cos (x) - sin (x)) = - sin (x) - cos (x)

= 2 (e^{x} (cos (x) - sin (x)) + (- sin (x) - cos (x)) e^{x})

Vereinfache

2 (e^{x} (cos (x) - sin (x)) + (- sin (x) - cos (x)) e^{x}) : - 4 e^{x} sin (x)

= - 4 e^{x} sin (x)

s l o p e in t erce pt (3, 4), (5, - 4)

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\int 1 - cos (4 x) d x