derivative of ax^3+bx^2-c/3 x+d

Lösung

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

3 a x^{2} + 2 b x - \frac{c}{3}

Schritte zur Lösung

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

Vereinfache

a x^{3} + b x^{2} - \frac{c}{3} x + d : a x^{3} + b x^{2} - \frac{c x}{3} + d

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (\frac{c x}{3}) = \frac{c}{3}

\frac{dd}{d x} = 0

= 3 a x^{2} + 2 b x - \frac{c}{3} + 0

Vereinfache

= 3 a x^{2} + 2 b x - \frac{c}{3}

d er i v a t i v e y = x^{2} (x - 1)

\frac{\partial}{\partial x} (x^{7} y^{9} - x^{6} y^{8})

\int \frac{1}{( x ^{2} + x + 1 )} d x

t a y l or (- 5 x + 24)^{\frac{3}{2}}

a re a f (x) = 4 - (x - 1)^{2}, (1, 3)