derivative y=x^6cos(x)

Lösung

ableitung von

y = x^{6} cos (x)

6 x^{5} cos (x) - x^{6} sin (x)

Schritte zur Lösung

\frac{d}{d x} (x^{6} cos (x))

Wende die Produktregel an:

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

f = x^{6}, g = cos (x)

= \frac{d}{d x} (x^{6}) cos (x) + \frac{d}{d x} (cos (x)) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} cos (x) + (- sin (x)) x^{6}

Vereinfache

= 6 x^{5} cos (x) - x^{6} sin (x)

e^{x} (y^{3} + x y^{3} + 1) d x + 3 y^{2} (x e^{x} - 6) d y = 0

s l o p e (- 7, 6), (9, - \frac{6}{7})

x \to \infty lim (3 x - x^{2})

8 y^{^{''}} + 6 y^{^{'}} - y = 11

h \to 0 lim (cos (\frac{π}{2}))