derivative 3xsin(x)

Lösung

ableitung von

3 x sin (x)

3 (sin (x) + x cos (x))

Schritte zur Lösung

\frac{d}{d x} (3 x sin (x))

Entferne die Konstante:

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

= 3 \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)

= 3 (\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)

= 3 (1 \cdot sin (x) + cos (x) x)

Vereinfache

= 3 (sin (x) + x cos (x))

\frac{d}{d x} ((\frac{x ^{2} + 4}{x ^{2} - 4})^{5})

\frac{d}{d x} (x^{s i n^{2} (x)})

\frac{d}{d a} (\frac{π ( 9 a ^{2} - 1 )}{54 a ^{2}})

\frac{\partial}{\partial x} (5)

\frac{d y}{d x} - \frac{( y ^{2} - x ^{2} )}{3 x y} = 0