derivative of sin(x-xsin(y))

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

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

x \to 4 lim (\frac{2 x + 1}{3 x + 3})

\frac{d y}{d x} = \frac{e ^{x}}{y}

\int_{- \infty}^{18} x e^{\frac{x}{9}} d x

\frac{d}{d x} ((x^{2} - 10 x + 9) 25 - x^{2})

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