derivative of 10xsin(x)

Lösung

\frac{d}{d x} (10 x sin (x))

10 (sin (x) + x cos (x))

Schritte zur Lösung

\frac{d}{d x} (10 x sin (x))

Entferne die Konstante:

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

= 10 \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)

= 10 (\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)

= 10 (1 \cdot sin (x) + cos (x) x)

Vereinfache

= 10 (sin (x) + x cos (x))

9 x^{2} y^{2} + x^{\frac{3}{2}} y^{^{'}} = y^{2}

d er i v a t i v e (x^{2} - 18) (2 x + 3)

\int x + \frac{1}{x ^{2}} d x

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

\frac{\partial}{\partial y} ((x^{2} - 1) (y + 2))