derivative of 4e^xsin(x)

Lösung

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

4 (e^{x} sin (x) + cos (x) e^{x})

Schritte zur Lösung

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

Entferne die Konstante:

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

= 4 \frac{d}{d x} (e^{x} sin (x))

Wende die Produktregel an:

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

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

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

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

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

= 4 (e^{x} sin (x) + cos (x) e^{x})

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

\int x^{2} \cdot ln (2 x) d x

x \to 2 lim (\frac{3 x - 2}{x - 8})

\int_{0}^{1} \frac{1}{x ^{\frac{19}{18}}} d x

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