derivative of x^3+(3-3x^2^2+4)

Lösung

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

36 x^{3} + 3 x^{2} - 36 x

Schritte zur Lösung

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

Vereinfache

x^{3} + (3 - 3 x^{2})^{2} + 4 : 9 x^{4} + x^{3} - 18 x^{2} + 13

= \frac{d}{d x} (9 x^{4} + x^{3} - 18 x^{2} + 13)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (9 x^{4}) + \frac{d}{d x} (x^{3}) - \frac{d}{d x} (18 x^{2}) + \frac{d}{d x} (13)

\frac{d}{d x} (9 x^{4}) = 36 x^{3}

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

\frac{d}{d x} (18 x^{2}) = 36 x

\frac{d}{d x} (13) = 0

= 36 x^{3} + 3 x^{2} - 36 x + 0

Vereinfache

= 36 x^{3} + 3 x^{2} - 36 x

\frac{d y}{d x} + y = x^{2} - 2

x \to 2 lim (sin (\frac{π x}{2}))

\int \frac{1}{u ^{\frac{3}{2}}} d u

d er i v a t i v e 2 sin^{2} (6 x^{4})

\frac{d}{d x} (\frac{x - 4}{x ^{2} + 1})