(\partial)/(\partial x)((-(3x+9))^9)

Lösung

\frac{\partial}{\partial x} ((- (3 x + 9))^{9})

- 177147 x^{8} - 4251528 x^{7} - 44641044 x^{6} - 267846264 x^{5} - 1004423490 x^{4} - 2410616376 x^{3} - 3615924564 x^{2} - 3099363912 x - 1162261467

Schritte zur Lösung

\frac{\partial}{\partial x} ((- (3 x + 9))^{9})

Vereinfache

(- (3 x + 9))^{9} : - 19683 x^{9} - 531441 x^{8} - 6377292 x^{7} - 44641044 x^{6} - 200884698 x^{5} - 602654094 x^{4} - 1205308188 x^{3} - 1549681956 x^{2} - 1162261467 x - 387420489

= \frac{\partial}{\partial x} (- 19683 x^{9} - 531441 x^{8} - 6377292 x^{7} - 44641044 x^{6} - 200884698 x^{5} - 602654094 x^{4} - 1205308188 x^{3} - 1549681956 x^{2} - 1162261467 x - 387420489)

Wende die Summen-/Differenzregel an:

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

= - \frac{\partial}{\partial x} (19683 x^{9}) - \frac{\partial}{\partial x} (531441 x^{8}) - \frac{\partial}{\partial x} (6377292 x^{7}) - \frac{\partial}{\partial x} (44641044 x^{6}) - \frac{\partial}{\partial x} (200884698 x^{5}) - \frac{\partial}{\partial x} (602654094 x^{4}) - \frac{\partial}{\partial x} (1205308188 x^{3}) - \frac{\partial}{\partial x} (1549681956 x^{2}) - \frac{\partial}{\partial x} (1162261467 x) - \frac{\partial}{\partial x} (387420489)

\frac{\partial}{\partial x} (19683 x^{9}) = 177147 x^{8}

\frac{\partial}{\partial x} (531441 x^{8}) = 4251528 x^{7}

\frac{\partial}{\partial x} (6377292 x^{7}) = 44641044 x^{6}

\frac{\partial}{\partial x} (44641044 x^{6}) = 267846264 x^{5}

\frac{\partial}{\partial x} (200884698 x^{5}) = 1004423490 x^{4}

\frac{\partial}{\partial x} (602654094 x^{4}) = 2410616376 x^{3}

\frac{\partial}{\partial x} (1205308188 x^{3}) = 3615924564 x^{2}

\frac{\partial}{\partial x} (1549681956 x^{2}) = 3099363912 x

\frac{\partial}{\partial x} (1162261467 x) = 1162261467

\frac{\partial}{\partial x} (387420489) = 0

= - 177147 x^{8} - 4251528 x^{7} - 44641044 x^{6} - 267846264 x^{5} - 1004423490 x^{4} - 2410616376 x^{3} - 3615924564 x^{2} - 3099363912 x - 1162261467 - 0

Vereinfache

= - 177147 x^{8} - 4251528 x^{7} - 44641044 x^{6} - 267846264 x^{5} - 1004423490 x^{4} - 2410616376 x^{3} - 3615924564 x^{2} - 3099363912 x - 1162261467

d er i v a t i v e f (x) = 5 x - 6 x^{2}

d er i v a t i v e f (x) = e^{π} + π^{x}

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

\int \frac{3 + z}{1 - z ^{2}} d z

n = 0 \sum \infty \frac{1}{n ^{2}} x^{n}