derivative of 3x*sin(x)

Lösung

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

d er i v a t i v e \frac{( x )}{4 + x}

d er i v a t i v e 0.49489 n v^{2} + 1500 \cdot \frac{n}{v}

\int 3 x^{2} + 8 x d x

\frac{\partial}{\partial x} (6 x y^{2})

\frac{\partial}{\partial x} (sin (2 y - 5 x))