derivative of 25xsin(11x)

Lösung

\frac{d}{d x} (25 x sin (11 x))

25 (sin (11 x) + 11 x cos (11 x))

Schritte zur Lösung

\frac{d}{d x} (25 x sin (11 x))

Entferne die Konstante:

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

= 25 \frac{d}{d x} (x sin (11 x))

Wende die Produktregel an:

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

f = x, g = sin (11 x)

= 25 (\frac{d x}{d x} sin (11 x) + \frac{d}{d x} (sin (11 x)) x)

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

\frac{d}{d x} (sin (11 x)) = cos (11 x) \cdot 11

= 25 (1 \cdot sin (11 x) + cos (11 x) \cdot 11 x)

Vereinfache

= 25 (sin (11 x) + 11 x cos (11 x))

\int 3 x^{2} e^{x^{3}} d x

\frac{d}{d x} (3 x - 6 x)

\int_{1}^{\infty} \frac{1}{x ^{3}} d x

\frac{d}{d x} (x^{2} y^{5})

\int_{0}^{\infty} (a + f (x)) d x