derivative of x^4-4x^3+6x^2-36x+27

Lösung

\frac{d}{d x} (x^{4} - 4 x^{3} + 6 x^{2} - 36 x + 27)

4 x^{3} - 12 x^{2} + 12 x - 36

Schritte zur Lösung

\frac{d}{d x} (x^{4} - 4 x^{3} + 6 x^{2} - 36 x + 27)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (6 x^{2}) - \frac{d}{d x} (36 x) + \frac{d}{d x} (27)

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

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (36 x) = 36

\frac{d}{d x} (27) = 0

= 4 x^{3} - 12 x^{2} + 12 x - 36 + 0

Vereinfache

= 4 x^{3} - 12 x^{2} + 12 x - 36

\frac{d}{d x} (\frac{1 + csc ( x )}{1 + sec ( x )})

t an g e n t (1 + 4 x)^{\frac{3}{2}}

\frac{d}{d x} (\frac{11 x}{2 + x ^{2}})

\int_{0}^{10} 49 - 9.8 x d x

d er i v a t i v e y = (\frac{x ^{2} + 4}{x ^{2} - 4})^{4}