derivative of cos(x+x*sin(x))

Lösung

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

x cos (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= - sin (x) + sin (x) + x cos (x)

Vereinfache

= x cos (x)

d er i v a t i v e f (x) = (x^{3} + 8) e^{x}

s l o p e y = \frac{16}{( x + 4 ) ^{2}}, (0, 1)

x \to 2 lim (\frac{1}{3.9})

a re a y = tan (x), y = - 3 tan (x), x = \frac{π}{4}

x \to 0 lim (\frac{9 ^{x} - 1 3 ^{x}}{x})