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})

\int \frac{1}{x ^{4} 16 - 25 x ^{2}} d x

\frac{d}{d x} (\frac{x ^{2} - 16}{x + 4})

d er i v a t i v e (x^{2} + 3) (x^{2} - 3) x^{2}

\int sec^{2} (x) tan^{2} (x) d x

\frac{\partial}{\partial x} (- \frac{1}{x - y})