derivative of 1/6 (x-1(x+5)^5+10)

Lösung

\frac{d}{d x} (\frac{1}{6} (x - 1) (x + 5)^{5} + 10)

x (x + 5)^{4}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{6} (x - 1) (x + 5)^{5} + 10)

Vereinfache

\frac{1}{6} (x - 1) (x + 5)^{5} + 10 : \frac{( x + 5 ) ^{5} ( x - 1 )}{6} + 10

= \frac{d}{d x} (\frac{( x + 5 ) ^{5} ( x - 1 )}{6} + 10)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{( x + 5 ) ^{5} ( x - 1 )}{6}) + \frac{d}{d x} (10)

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

\frac{d}{d x} (10) = 0

= x (x + 5)^{4} + 0

Vereinfache

= x (x + 5)^{4}

t an g e n t y = 9 x^{2} + 9 x - 3

d er i v a t i v e f (x) = sin (1 + cos (x))

\int_{0}^{1} \frac{14}{4 y - 1} d y

\frac{d}{d p} (ln (p))

\int x x - 3 d x