derivative of-3/2 x^4cos(x)

Lösung

\frac{d}{d x} (- \frac{3}{2} x^{4} cos (x))

- \frac{3}{2} (4 x^{3} cos (x) - x^{4} sin (x))

Schritte zur Lösung

\frac{d}{d x} (- \frac{3}{2} x^{4} cos (x))

Vereinfache

- \frac{3}{2} x^{4} cos (x) : - \frac{3 x ^{4} cos ( x )}{2}

= \frac{d}{d x} (- \frac{3 x ^{4} cos ( x )}{2})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{3}{2} \frac{d}{d x} (x^{4} cos (x))

Wende die Produktregel an:

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

f = x^{4}, g = cos (x)

= - \frac{3}{2} (\frac{d}{d x} (x^{4}) cos (x) + \frac{d}{d x} (cos (x)) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= - \frac{3}{2} (4 x^{3} cos (x) + (- sin (x)) x^{4})

Vereinfache

= - \frac{3}{2} (4 x^{3} cos (x) - x^{4} sin (x))

a re a x^{2}, x

\int_{0}^{5} x^{3} d x

y^{^{''}} x^{2} - 5 x y^{^{'}} + 9 y = 0

l a pl a ce t r an s f or m cos^{2} (k t)

\int_{0}^{3} 3 d x