derivative 5-(x-9)^4

Lösung

ableitung von

5 - (x - 9)^{4}

- 4 x^{3} + 108 x^{2} - 972 x + 2916

Schritte zur Lösung

\frac{d}{d x} (5 - (x - 9)^{4})

Vereinfache

5 - (x - 9)^{4} : - x^{4} + 36 x^{3} - 486 x^{2} + 2916 x - 6556

= \frac{d}{d x} (- x^{4} + 36 x^{3} - 486 x^{2} + 2916 x - 6556)

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (x^{4}) + \frac{d}{d x} (36 x^{3}) - \frac{d}{d x} (486 x^{2}) + \frac{d}{d x} (2916 x) - \frac{d}{d x} (6556)

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

\frac{d}{d x} (36 x^{3}) = 108 x^{2}

\frac{d}{d x} (486 x^{2}) = 972 x

\frac{d}{d x} (2916 x) = 2916

\frac{d}{d x} (6556) = 0

= - 4 x^{3} + 108 x^{2} - 972 x + 2916 - 0

Vereinfache

= - 4 x^{3} + 108 x^{2} - 972 x + 2916

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{7}{x ^{4}}) (x + 5 x^{3}))

\int x^{3} cos^{2} (x) d x

\int \frac{1}{4 ^{2} - x ^{2}} d x

d er i v a t i v e \frac{t}{( t - 6 ) ^{2}}

x \to - 8 - lim (\frac{∣ x + 8 ∣}{x + 8})