derivative of-x^3+5ax^2-3a^2x-b

Lösung

\frac{d}{d x} (- x^{3} + 5 a x^{2} - 3 a^{2} x - b)

- 3 x^{2} + 10 a x - 3 a^{2}

Schritte zur Lösung

\frac{d}{d x} (- x^{3} + 5 a x^{2} - 3 a^{2} x - b)

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (x^{3}) + \frac{d}{d x} (5 a x^{2}) - \frac{d}{d x} (3 a^{2} x) - \frac{d b}{d x}

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

\frac{d}{d x} (5 a x^{2}) = 10 a x

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

\frac{d b}{d x} = 0

= - 3 x^{2} + 10 a x - 3 a^{2} - 0

Vereinfache

= - 3 x^{2} + 10 a x - 3 a^{2}

d er i v a t i v e e^{t} cos (3 t)

\frac{\partial}{\partial y} (\frac{x}{1 + y})

y^{^{''}} - 10 y^{^{'}} + 2 y = 0

\frac{\partial}{\partial z} (\frac{x}{y + z})

l a pl a ce t r an s f or m 4 sin (π t)