derivative (1+cos^3(x^7))^{12}

Lösung

ableitung von

(1 + cos^{3} (x^{7}))^{12}

- 252 x^{6} cos^{2} (x^{7}) sin (x^{7}) (1 + cos^{3} (x^{7}))^{11}

Schritte zur Lösung

\frac{d}{d x} ((1 + cos^{3} (x^{7}))^{12})

Wende die Kettenregel an:

12 (1 + cos^{3} (x^{7}))^{11} \frac{d}{d x} (1 + cos^{3} (x^{7}))

= 12 (1 + cos^{3} (x^{7}))^{11} \frac{d}{d x} (1 + cos^{3} (x^{7}))

\frac{d}{d x} (1 + cos^{3} (x^{7})) = - 21 x^{6} cos^{2} (x^{7}) sin (x^{7})

= 12 (1 + cos^{3} (x^{7}))^{11} (- 21 x^{6} cos^{2} (x^{7}) sin (x^{7}))

Vereinfache

= - 252 x^{6} cos^{2} (x^{7}) sin (x^{7}) (1 + cos^{3} (x^{7}))^{11}

\frac{\partial}{\partial x} (y^{3} sin (6 x))

t an g e n t f (x) = \frac{2}{3 x + 5}, (- 1, 1)

x \to 0 lim (\frac{x ^{2} + 7 x}{x})

\int (2 t + 3)^{- 3} d t

t an g e n t f (x) = \frac{2 x - 1}{x + 5}, at x = 4