derivative of-xsin(xy)

Lösung

\frac{d}{d x} (- x sin (x y))

- sin (x y) - x cos (x y) y - x^{2} cos (x y) \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (- x sin (x y))

Entferne die Konstante:

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

= - \frac{d}{d x} (x sin (x y))

Wende die Produktregel an:

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

f = x, g = sin (x y)

= - (\frac{d x}{d x} sin (x y) + \frac{d}{d x} (sin (x y)) x)

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

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

= - (1 \cdot sin (x y) + cos (x y) (y + x \frac{d y}{d x}) x)

Vereinfache

- (1 \cdot sin (x y) + cos (x y) (y + x \frac{d y}{d x}) x) : - sin (x y) - x cos (x y) y - x^{2} cos (x y) \frac{d y}{d x}

= - sin (x y) - x cos (x y) y - x^{2} cos (x y) \frac{d y}{d x}

2 x \frac{d y}{d x} = y + 1

\int_{4}^{6} 0.2 e^{- 0.2 x} d x

x \to 3 lim (\frac{sin ( 3 x )}{x})

\int \frac{x}{( x ^{2} + 6 ) ^{2}} d x

\frac{\partial}{\partial x} (3 e^{s i n (x + 4 c t)})