derivative f(x)=(1+cos^2(x))^7

Lösung

ableitung von

f (x) = (1 + cos^{2} (x))^{7}

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

Schritte zur Lösung

\frac{d}{d x} ((1 + cos^{2} (x))^{7})

Wende die Kettenregel an:

7 (1 + cos^{2} (x))^{6} \frac{d}{d x} (1 + cos^{2} (x))

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

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

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

Vereinfache

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

\frac{\partial ^{2}}{\partial u ( v ) \partial v} (8 v e^{- 6 u (v)})

\int \frac{2 cos ( x )}{- 2 + 6 sin ( x )} d x

d er i v a t i v e \frac{16 x}{x ^{2} + 16}

d er i v a t i v e 7 x^{2} e^{x}

t an g e n t f (x) = - 4 (2 x + 7)^{- 5} (2), at x = 2