derivative (1+cos^2(x))^5

Lösung

ableitung von

(1 + cos^{2} (x))^{5}

- 5 sin (2 x) (1 + cos^{2} (x))^{4}

Schritte zur Lösung

\frac{d}{d x} ((1 + cos^{2} (x))^{5})

Wende die Kettenregel an:

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

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

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

= 5 (1 + cos^{2} (x))^{4} (- sin (2 x))

Vereinfache

= - 5 sin (2 x) (1 + cos^{2} (x))^{4}

n = 0 \sum \infty \frac{( e ^{n} )}{5}

\frac{d}{d x} (- 8 x^{3})

\int_{\frac{1}{7}}^{5} 6 x ln (7 x) d x

x \to \frac{π}{2} lim (x \cdot sec (x))

\frac{d}{d x} (- \frac{2 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}})