derivative of 8xsin(x)

Lösung

\frac{d}{d x} (8 x sin (x))

8 (sin (x) + x cos (x))

Schritte zur Lösung

\frac{d}{d x} (8 x sin (x))

Entferne die Konstante:

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

= 8 \frac{d}{d x} (x sin (x))

Wende die Produktregel an:

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

f = x, g = sin (x)

= 8 (\frac{d x}{d x} sin (x) + \frac{d}{d x} (sin (x)) x)

\frac{d x}{d x} = 1

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

= 8 (1 \cdot sin (x) + cos (x) x)

Vereinfache

= 8 (sin (x) + x cos (x))

x \to - 3 + lim (\frac{x - 3}{x - 4})

\frac{d}{d x} (\frac{e ^{x^{2}}}{( 2 x + 1 ) ^{5}})

\frac{\partial}{\partial y} (4 x y^{3})

n = 1 \sum \infty \frac{2}{n \cdot ( n + 2 )}

f (x) = 2 sec (x)