derivative of xsin(x+y+ycos(x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\frac{d}{d t} (\frac{t}{1 + t ^{2}})

a re a x^{2}, 1, 0

t an g e n t f (x) = 9 x^{2} + 7 x - 6

\int \frac{1}{t ^{2} 169 - t ^{2}} d t

n or ma l y = \frac{x}{x + 6}, (4, 0.2)