derivative cos(x)x^3

Lösung

ableitung von

cos (x) x^{3}

- x^{3} sin (x) + 3 x^{2} cos (x)

Schritte zur Lösung

\frac{d}{d x} (cos (x) x^{3})

Wende die Produktregel an:

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

f = cos (x), g = x^{3}

= \frac{d}{d x} (cos (x)) x^{3} + \frac{d}{d x} (x^{3}) cos (x)

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

= (- sin (x)) x^{3} + 3 x^{2} cos (x)

Vereinfache

= - x^{3} sin (x) + 3 x^{2} cos (x)

y^{^{''}} - 12 y^{^{'}} + 36 y = t e^{6 t}

\frac{d}{d x} (\frac{2 + sin ( x )}{2 x + cos ( x )})

5 t \frac{d y}{d t} - 5 y = t

\frac{\partial}{\partial y} (\frac{y}{x ^{2} + y ^{2}})

\frac{\partial}{\partial x} (x^{3} z + yz)