derivative of 9e^x(cos(x-sin(x)))

Lösung

\frac{d}{d x} (9 e^{x} (cos (x) - sin (x)))

- 18 e^{x} sin (x)

Schritte zur Lösung

\frac{d}{d x} (9 e^{x} (cos (x) - sin (x)))

Entferne die Konstante:

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

= 9 \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)

= 9 (\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)

= 9 (e^{x} (cos (x) - sin (x)) + (- sin (x) - cos (x)) e^{x})

Vereinfache

9 (e^{x} (cos (x) - sin (x)) + (- sin (x) - cos (x)) e^{x}) : - 18 e^{x} sin (x)

= - 18 e^{x} sin (x)

\int (cos (x) + 5^{x}) d x

\int (x^{2} + 6 x) cos (x) d x

\frac{d}{d x} (e^{a x^{6}})

d er i v a t i v e f (x) = (x)^{3} \cdot e^{(3 x)}

2 y^{2} = \frac{d y}{d x}