derivative of x^6-4x^5+5x^4-5x^2+4x-1

Lösung

\frac{d}{d x} (x^{6} - 4 x^{5} + 5 x^{4} - 5 x^{2} + 4 x - 1)

6 x^{5} - 20 x^{4} + 20 x^{3} - 10 x + 4

Schritte zur Lösung

\frac{d}{d x} (x^{6} - 4 x^{5} + 5 x^{4} - 5 x^{2} + 4 x - 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{6}) - \frac{d}{d x} (4 x^{5}) + \frac{d}{d x} (5 x^{4}) - \frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (4 x) - \frac{d}{d x} (1)

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (4 x^{5}) = 20 x^{4}

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

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

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

\frac{d}{d x} (1) = 0

= 6 x^{5} - 20 x^{4} + 20 x^{3} - 10 x + 4 - 0

Vereinfache

= 6 x^{5} - 20 x^{4} + 20 x^{3} - 10 x + 4

\int_{1}^{5} 4 r^{2} ln (r) d r

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

\int (x^{3} - 6 x - 9) d x

d er i v a t i v e f (x) = \frac{4 x}{( x - 9 ) ^{5}}

t a y l or ln (4 x), 1